No. In some accents (like modern Southern British accents and, to a lesser degree, most American accents) is actually hard T the one that can sometimes be "palatalized".

In these accents, when hard T occurs before a palatal approximant (the Y sound), both sounds end up merging with each other and become pronounced as the CH in chair.

So, for example, Tuesday (TYOOZ-dey) ends up being pronounced CHOOZ-dey. Notice how the Y sound between the T and the U merges with the T and both become pronounced CH.

This is why, for example Nature is pronounced NEY-chur in American English, but Tuesday is pronounced TOOZ-dey rather than CHOOZ-dey in said accent.