The answers by @CamilleGoudeseune and @YeeteshPulstya are on point, but I would like to add a little to them.
Beginners training to sing in the Indian classical music system typically have difficulty identifying the position of an arbitrary swaram. The harmonium is a useful aid at this stage since:
- it is a keyed instrument, so even a beginner can reproduce notes on it very easily, and
- it does not require regular re-tuning, which can be an arduous (or even impossible) task for a beginner.
Singing along with the harmonium will help solidify a mental image of the swara-sthānams (positions of the notes) in one's mind, a basic aspect of swara jnyānam (literally, "knowledge of the swaras").
However, do not forget that Indian classical music makes use of more than just the sapta swaras (seven notes), but instead identifies many microtones called shrutis, which may number twenty-two or even more. As you continue to practise and listen to music, you will develop your "mental ear" to identify the positions of not only the sapta swaras, but also each of the shrutis (this is called kelvi jnyānam in south India, literally "knowledge obtained by listening").
So, the fear that the tempered scale will be impressed upon your mind instead of the harmonic scale is unfounded. With continued practice, you will be able to identify by ear not only the subtle differences between these two tunings, but also the shrutis which cannot be reproduced on the harmonium by any of the individual keys.
The practice of the basic exercises, alankārams included, is of paramount importance in improving one's swara jnyānam. This cannot be emphasised enough. There is absolutely no way forward without practising the basic exercises so thoroughly that you can deliver them in multiple scales and speeds with ease. Practise, practise, practise!
It is also worth mentioning the value of the harmonium as a concert level instrument, in light of some answers and comments that deem it to be a beginner's instrument meant to be graduated from.
It is a common misconception that a keyed instrument like the harmonium does not have a place in Indian classical music which is so gamaka (oscillation) laden; at most it could be effective as an accompaniment in kirtans and bhajans.
However, nothing could be further from the truth! I offer below my (rough and liberal) translation from Thamizh (Tamil) of some of the words of the great vidwān (master) Madurai T. N. Seshagopalan:
Shruti is that which lies within the swaras. If one plays or sings gamaka-shruti-vishada rāgams without gamakas (oscillations), then one cannot bring out the true aural form of that rāgam (in contrast to sva-sthāna-vishada rāgams). But, by playing the swarams along with their anuswarams the way they are meant to be played, one can create—in this vādyam (musical instrument)—the illusion of gamakas.
In the past, the harmonium was a "banned instrument". I honestly do not understand why it was so. My guru used to say that when Bade Ghulam Ali Khan's father would play the harmonium, one would be terrified to even gaze upon him after that—such was his mastery over the instrument. S. G. Kalanchandra Kittappa would host Rajarathnam Pillai (the legendary nadaswaram vidwan) at his home in Senkottai just because the latter so desired to hear Kittappa's elder brother S. G. Kasi Iyer play the harmonium. Such was the calibre of the masters of yore.
Today, I have not taken up this instrument merely for doing some "swara jugglery". On this instrument, rāgams such as Yadukula Kāmbhoji, Nāyaki, Neelāmbari, Begada, Bhairavi, Thodi, Dhanyāsi can be played while remaining true to their swarupam (form).
. . .
One can say this this is also one of the ancient musical instruments of this culture, even though it was introduced from a foreign land. Since the harmonium can be used to produce a "continuous" sound, it is indeed an instrument eligible for playing Carnatic music.
Source: concert in memory of Alathur Venkatesa Iyer, held at the Arkay Convention Centre under the aegis of Madhuradhwani, on 24 September, 2016. Accompaniments: M. Chandrasekaran on the violin and Trichur Narendran on the mridangam. Link to the full concert here. Speech of T. N. Seshagopalan starts at 1:05:46, ends at 1:10:13.
In addition to the brilliant concert from which the above speech is extracted (in which Seshagopalan performs the rāgams Goulai, Ānandabhairavi, Varamu, Yadukula Kāmbhoji, Bhairavi, Hemavati, Sindubhairavi and Sourāshtram), it is worth listening to the following recordings to get a sense of the immense scope of the harmonium in Indian classical music:
- Live concert of Madurai T. N. Seshagopalan on the harmonium, held at the Arkay Convention Centre, under the aegis of Brahma Gana Sabha & BGS Trust, on 31 December, 2016. Accompaniments: M. Chandrasekaran on the violin and Neyveli Venkatesh on the mridangam. Seshagopalan performs the rāgams Nāttai, Reetigoulai, Hameer Kalyāni, Hindolam, Asāveri, Neelāmbari, Kharaharapriya, Madhuvanti and Sri.
- Live recording of Muthu Natesa Bhagavathar on the harmonium, held in Mumbai (then Bombay) in 1968. Accompaniments: K. Shivakumar on the violin and P. S. Devarajan on the mridangam. Released by Country and Eastern in 2011 under the title Karnatik Harmonium. Bhagavathar performs the rāgams Begada, Hamsadhwani, Sri Ranjani and Poorvikalyani.
My (late) guru Bombay V. Vamanan once performed an All India Radio (AIR) concert with harmonium on accompaniment instead of violin. It was aired on 21st July, 2012. The accompaniments were S. Krishnan on the harmonium and P. Murugan on the mridangam. My guru performed the ragams Māyāmālavagoulai, Vāchaspati, Sāveri and Begada. At the moment, I only have an audio cassette tape recording of this AIR concert, and so I am unable to share any link to it.