In theory, yes, minimizing may help as it uses fewer refreshes to the screen so less ram is used. In actuallity, I'm not positive about that since you are going through Direct X or Open GL, which may be rendering to a buffer regardless of whether or not it's actually on screen.
One thing I will say, if you have Windows Task Manager up, especially if it's in the CPU Usage Screen with the constantly changing graph, it's a really good idea to minimize that since that does eat more ram if it's not minimized. Also, it's a good idea to shut down as many other apps as possible. I usually keep one IE window open to view forums here, one windows folder open that shows where I'm recording to, and close all other apps except the recording program.
I use Internet Explorer since I think it uses the same ram chunk allocated to windows explorer... if you use another app for browsing, like foxfire or mozilla, closing those alternatives down may be a good idea when recording since they use another, seperate chunk of ram, which is using ram that you could be allocating to the recording program. Also, try to stay offline as much as possible. I mainly use my wife's computer when she's not there to surf while recording.
Of course, I'm only on a 1.5 ghz machine with 512 mb of ram at home, and am using ati's recording program, recording to vcd quality, so you might be able to get away with having more open if you have a faster machine, but maybe not if you are recording at dvd quality or higher... True DVD quality maxes my machine out, and burns a lot of hdd space, so I just use vcd quality most of the time.
If it gets to be too much of a problem, try maximizing your computer's power by shutting down unneeded stuff... There's some list somewhere that came out a couple years ago that shows how to really maximize your computer by shutting off a lot of resources that you don't need. I think it was some website from some dude that went by the name blackviper.
edit:
Googled it... Here you go...
http://web.archive.org/web/20041128084144/www.blackviper.com/WinXP/servicecfg.htm
http://www.google.com/search?hl=en&lr=&q=black+viper+services+xp
Really good and useful info there. Be careful when shutting off services that you aren't absolutely positive if you need or not since it could kill some programs and stuff if you aren't careful with what you are doing.