BIF with a Big lens is fun - NOT!
It is certainly do-able - I frequently do so! However the birds do need to be further out (with the inevitable IQ compromises) but it can work well.
You must also factor in the extra weight and expense. It is not just the lens (the one you mention is a bit of a monster) but also a good gimbal head and a top quality tripod. All of this is heavy and expensive - trust me my primary set up is of this type but with the "lightweight" Canon 800 F5.6 L IS. The lack of IS on the lens is irrelevant for this sort of use - it just gets in the way and mucks up AF acquisition and tracking for BIF.
As another poster mentioned - you will be unlikely to get the 600 F4 L (non IS) repaired if it fails as parts are no longer made. That does not necessarily mean that you shouldn't buy it, just don't pay much!
My personal choices for BIF are the Canon 300 F4 L IS (IS off), Canon 400 F5.6 L, Canon 100-400 L IS Mk2 (IS off) or, if your arms are up to it, the Canon 300 F2.8 L (either IS version). The 300 F2.8 lenses are often shorter than what is ideal but they take 1.4 extenders remarkably well with little loss of AF performance (still better than the others mentioned) and when used as a bare lens are unbeatable IMO. Pretty much the best/fastest AF going and some of the sharpest lenses made.
Just my thoughts.