I think it should work if you set it up not to use swap space and got enough memory. Though I don't know how would you launch programs as there is no hdd to read from. manipulating root would also be inpossible I guess.
Anyway whatever you load in the memory should stay there as long as it's needed(programs running) or system restart/shutdown.
Try to opt for a lightweight setup if you can(xfce,lxde,or no windowing system).
HDD is not needed for a computer to work, though it's helpful, I remember when we used to boot from floppy or network (DOS).

Please note that I'm a Linux noob.