AFAIK most of the pressure is around RSU expiration, not options. So - no (Unless we're talking about Stripe changing this equity program even further)
It sounds like Stripe is going to declare a qualifying event which will convert outstanding RSUs into shares which will bring along with it a major tax implication for the RSU holders, who would be in a really tough spot if they got a windfall of totally illiquid Stripe equity. So Stripe is going to buy shares to facilitate tax withholding, for which they need the $$ they are raising.