The short answer is no, they are not very flexible. However, there are some options.
Yosemite has a small, totally un-publicized campground that is for folks the day before/after their backpacking permit, that allows bike camping. You do have to pay to camp, but I think it is pretty easy to arrange, and I have never seen more than a few tents there, even in mid-season. (used to go there a lot, the valley in valygrl is yosemite valley)
There's also Camp 4, which is walk-in, but extremely crowded in the spring/summer months. Be in line at 6:30 am to secure a spot.
You can sometimes get day-of sites in the pines campgrounds by waiting in line for the no-show sites to be distributed, in the Curry Village parking lot, but that is very iffy. I think it happens at 4:00 or 4:30pm. If worst comes to very worst, ride around in the campground, look for someone who is sleeping in their RV/van, and nicely offer to pay for their site if you can use their tent spot. This will 99.99% work, but you didn't hear it from me.
If you are coming over Tioga Road, there are places to bivvy (be low-key) on the east side of the pass, just before the entrance station, there are campsites at the bottom of the pass just out of Lee Vining, the Tuolumne Meadows main campground holds half their sites for day-of (but get there early), and there are some more day-of (maybe??) sites between TM and Crane Flat. It think they are called Tamarack and White Wolf.
You really must take the bear/food regulations seriously in both these parks. If not camping in a designated site with a bear-proof box, you should have your own personal bear-proof container and make sure your panniers have never had any food in them.
Sorry, can't help w/sequoia, except to say there is a section of the road between sequoia and Kings Cyn that is in neither park, and is forest service, and allows camping. NO water or services, though.
Have a nice trip, and watch out for the rental RV's.