Of course it can, because sometimes with such a discount a very large percentage of the total amount of issued coins, tokens is sold. After all, when the token goes onto the exchange, the creators of the project try to make a price at which they bought at the final stages of the ICO, but they are hindered by early investors who sell everything, the only thing is that the tokens of early investors are blocked for a certain period, then it saves.
I believe that projects should freeze tokens of early investors for at least a year. this will give at least minimal stability for the token price
I think you are right, almost ICO/IEO projects which give a bonus to every early investors must have frozen their investor tokens for minimum 2 years. And yes as you said it can stabilize the price and also to avoid dumps at the beginning of their listing.