There are many ways to enjoy a music piece. It includes following rhythm only, enjoying melodic line only, or even complicated internal structure of the composition. Nobody can say what is right or not. However, in my opinion, the goal and purpose of performing the music is very important. Based on that, one can say, for the given purpose or goal what currently being done is serving the purpose well or poorly.
Segovia's transcript of Albeniz's work actually suffered loss of many important aspects of Albeniz's composition. However, when it was played on guitar, it made the other aspects of the work so beautiful. Many people started not caring about loss in the transcription - some even preferred guitar version better.
If you want participate in the joy of playing Asturias the way it enables you - without that tricky note, I think it is just fine. I think you can even give a concert with that arrangement.
However, if you want to convey the music Aleniz intended as close as possible (or representing Albeniz and what he wanted to say to the world) it is very different decision.
This is a very strange chord happening at the climax of the intro section. If you look at the chord in its isolation Sergio and 11684 are both right. A# can be seen as Bb, and yes they sound the same. In traditional harmonics they are two very different chords, but in the prime form they are the same chords. However, if you really want to understand what the chord is doing, you will need to understand the relationship with other parts of the music.
In Albeniz's original composition that A# (c# in piano) note was placed in the base and it is very audible. If you listen to the piano music, it is one of the dominant sounding notes happening at the climax of the intro that prepares for the next section (Piu lento, slow and quiet section, measure 63 - 122, 3/4 meter).
If you see the first section (measure 1 - 62) in a big picture, it almost sounds like there are two voices. One, for example, from measure 1 to 8 that starts with note E (G on piano), The other starts with note B (D on piano) from measure 9 to 16. This is a kind of the balance maintained in the begging. This structure even maintained and visible when it starts getting intense.
But, the measure you are asking about breaks this E-B balance. You get this strange chord with A#. As I mentioned previously, Albeniz placed this note in the base. This breaks E-B,E-B sequence suddenly by going to A# and create this wild sounding (almost out of place, very dissonant ) chord. If you hear E-B, E-B, and E-B many times and hear E-A# all of its sudden, you would go like "what the hack?" and want to hear B. It makes you wanting to hear B. Yes, you get B four measures later. This A# creates strong tendency of moving to B. It is serving as modulation bridge. This happens a lot. This is very common. It is just that Albeniz is using this in his own way. It is very clear and audible in original piano arrangement since A# is in the base. 4 measures after the chords with A#-C-E-G-Bb, the base in the piano does B-A#, B-A#, B-A# thing. I mentioned that the climax prepares for the next section. This B-A# maximizes this effect.
Guess what... the beginning note of the second section is B. We are in B minor land now. We were stably in E minor key, but we moved to B minor now. This is very common modulation, but I think Albeniz made it really special.
It was the limitation of guitar that Segovia could not place the A# in the base, but he was able to maintain it. I think it still sounds awesome - Segovia did really big favor to Asturias and Albeniz by recreating this tune on guitar.
I hope you get the idea of what you are going to do with that note A#. I think any decision is fine as long as you make the decision based on reasoning. I think you can even say "that A# does not do much in guitar arrangement, it is not very audible and there are plenty of other note make things work".
I tried to explain without getting too much in detail with the music theory. I hope I did not confuse you even further.
BTW, on the closing note, Albeniz really loved making his music colorful and loved all things about Spain.