I recommend against the upgrade, but it is probably "officially supported". I would definitely get the upgrade kit for your 3200 so you can upgrade software beyond what the original 3200 is capable of. The upgrade is 3200-MEM-UG and runs ~$400 list price (USD).
I use the CLI almost exclusively and have done many TFTP upgrades, but I have not done a 6.1.3.x upgrade on a non-XM 3200. I dont trust the new features without the additional memory.
As others have said, I have had to kill the session a couple times due to TFTP "hang ups", but it has never been a huge issue for me.
I typically watch the TFTP server and if I see the bytes in/out stalled, I will kill it and try again.