My understanding is that most do. At the very least, they're more lethargic for a while after eating.
I try to always feed my cats just before I konk off myself. That way I know they will not hassle me too much early in the morning looking for their next feed. They still hassle me, but wait a little longer before doing it. The picture of kitty paws up and belly exposed is what my black kitty does all the time (she's about 6 years old now). Always on her back. Been thinking I could make some money off her if I put a red light out as she's always on her back. But then who'd want 200 caterwauling males outside one's door? Something tells me they wouldn't exactly be paying customers.
So glad to hear Musica's thyroid meds kicked in and she's now doing well. Wonderful news, and I know the relief you are feeling. My oldest cat is now 18 years, so I know where you are coming from. We cherish each day now with our older kitties.