Is an SSD necessary in a budget gaming rig?

IMO, for a rig with a budget of $1000, it is almost essential, even if it is a small 60/64GB one as your boot drive and a few common programs, it is worth the speed. If your budget was more towards $500/$600 I would say it would be more valuable to save $75 on an SSD and put it towards a better GPU and have an SSD as your first upgrade down the line.

Sorry for rambling, I tend to do that ;P.
Short answer: for your budget, definitely.