Maverick looked up the info on “Someone Dear” himself during this part of the game. It seemed like a crucial choice to him at the time.
Disturbing the Chamber With ”Someone Dear” Resting – Should You Do It?
The short answer is yes.
The slightly longer answer is that you will have no choice but to do so. Without the help of the “Someone Dear”, you will not be able to proceed to the next floor. Despite the pleas of the Mysterious Voice, you will need to proceed into the stasis chamber.
The Illusion of Choice
Tower of Time has many moments of choice, some with bigger effects than others. This point in the game is not one of them. Without ignoring/going against the wishes of the Mysterious Voice, you will not be able to proceed much further.
I understand why you looked up this question, though. I did the same. The game presents it as a crucial choice. The Developers’ comment on it doesn’t really help, either. Although they seem to push you towards ignoring the Mysterious Voice, it is still very ambiguous. They don’t present it as being the only option at all. But it is, so feel free to proceed into the stasis chamber. Be warned that it is guarded, however.