To address the title, the answer is yes. You're in 12tet tuning, so you can play in one key, while everybody else is in another, and it'll all sound good. So if you can only play in, say, key C, you can re-tune your keyboard to any other key to fit - although getting it wrong is embarrassing.
You may find, as you make your way through the various keys, that some are easier to finger for some pieces, though. It hasn't always been thought through by the composer, so actually changing the key can be a good thing.
However, if you've learned a particular song in a partcular key, and the new vocalist doesn't want to sing there, it's easier to click the transpose button to find a suitable key than to play off the cuff in a new key. But being able to do that properly is way more impressive!
As others say, presented with an acoustic piano, without knowledge of all keys, you'll look a bit lame. So it's worth learning at least the more common keys and their scales.
I often see guitarists who cannot play without capos, and some of the reasons are risible. 'I learned it that way' is one. And if a guitarist has learned a song in open chords, using a capo sometimes won't rescue them from the mire. Being able to play barre chords properly will. Of course, there's always the case with guitar that capoed (?) chords sound different, and they do. So there is a good reason for use of capo on occasions. No real such argument for keyboardists, though. Except who would ever know?
I sometimes use the transpose the opposite way. After three or four songs in the same key, I'm getting fed up, so I'll hit the transpose button, and voila, I'm playing the next in a different key from the others, in a manner of speaking, and will then be able to sort of play in a different way, as well as alleviating the boredom. It's also a good way to brush up on the more unused keys than the guitar based E A D G and C. Unless the guitarists get out their capos...That sometimes fools me at open mics, when I see the 'open' chord shapes, but can't see where the capo is!
Become a better keyboard player, and learn all the scales, it'll benefit you in the end, and at the same time, learn to read in all keys, it'll put you well ahead of many others who own a keyboard!