During non-quota season, you can legally walk past the gate and dayhike anything you like. You can also write yourself a wilderness permit and do an overnight trip anywhere you like.
During quota season, you can legally dayhike just about anywhere without a permit, as long as you don’t enter the Whitney Zone. But you can’t enter the Whitney Zone without a permit. Entering the lottery and getting a reservation is one thing. You need the actual permit, issued by Inyo National Forest (not recreation.gov) to enter the Whitney Zone legally.
As Jim Lasos pointed out, you always have the option of deliberately breaking the rules. You may or may not get caught. If you get caught, you will probably be fined, and I heard that the fine was several hundred dollars more 20 years ago. If you need a rescue, they may be extra slow due to COVID-19, and the response for others may be extra slow due to your actions.
Now is not the time to be selfish. We should just follow the rules, and come back next year if we don’t get all our summits this year.