No. OSX assogns memory as necessary. If you run out of physical RAM, it will assign virtual memory from the hard drive and things will begin to slow down. Running out of memory usually does not cause crashes of the system, but there's a slight chance of have a quit on the application.
To see how much RAM you're, open an ID doc while any other regularly used apps are also launched. Then switch to Finder and go to GO menu/Utilities and click on Activity Monitor. Under Monitor menu click show activity monitor and then click on the memory tab in that. Don't panic if it shows an awful lot being used, osx swaps memroy from open but inactive programs to active programs as necessary.
I use a G4 1.25 mhz single processor powermac with 1.25 GB of RAM. Indesign, Photoshop, Illustrator, Acrobat, Safari, Entourage and Word are always on, sometimes more. I have no memory or performance problems