It's been that way for all the horses I've had gelded, even senior stallions, except for one who ended up jumping up with the clamps still on (former trainer turned her dogs out and "woke" him up early... grrr).
I had a 2 year old gelded last Thursday morning. Thursday evening we went out for an easy walk/jog behind the golf cart - he was practically pulling the cart ready to GO - and the next morning he went back to work. Most important for them to keep moving after the first day, to keep swelling down. He's done as well as any I've ever had gelded, and I think it's largely because I turned him out the next day between a stallion and a big mare LOL. He didn't know which one to harass so he spent the day running back and forth!
We usually have geldings done late in the day and the vet always says to keep them in their stall overnight and get them moving in the morning. I wouldn't put them pulling a heavy cart or going over high jumps, but just about anything else is good for them. I have had them gelded anywhere from 9 mos to 6 yrs of age and all have done very well.