I think sharing your expectations, at a minimum, will likely save time.
Most VCs have a range they are comfortable investing at, both in an absolute sene (e.g., “$3m is my biggest check” or “$20m pre is the highest we do), and also relative to a set of progress, risks, and metrics.
If you tell them a price they either have to beat, or meet … they’ll quick go into Price Mode. They will quickly tell you something they think will win, if they think they can win and can afford it.
And if the price is too high, they’ll beg off, but usually politely.
Here’s an example of where A16Z and Accel backed off in the Series B for Slack because the price was too high:
So yes, you can hide the ball and not share your target price and round size. That might, in some cases, get you a higher price. Perhaps VC #2 will bid against herself instead.
But it might also slow things down. If you already have a term sheet, you don’t have infinite time. I say, generally speaking, share your “ask”.