10A on the 12v rail is 120W, which is pretty sad if it's only one rail. At load, the HD 3850 seems to draw between 80-100W (well I think 98 is worst case), which doesn't leave much for your CPU and everything else. I doubt your PSU could even sustain the 10A on the 12v rail. I say no. Get a decent PSU if you want to upgrade your GPU. Is it even worth it for your system? What are you full specs?
"Fast" websearch says your CPU uses around 55W. That leaves you with ~60W. If you don't want to upgrade your PSU, I suggest a really weak GPU. You still have an AGP slot, so your probably looking at second hand. Because you have a weak CPU and GPU, you won't be gaming on this. Some sort of 9800?
I honestly wouldn't even bother with it. That Celeron is too slow to even make proper use of a Radeon 3650. Also, newer Radeon cards need hotfix drivers to work with those old AGP setups and they can be a bit of a pain to get to work. I say get a decent PSU you can reuse latter