No, you can get gain in the linear or transition regions - just not as
much, or as consistent.
A high bandwidth amp may work better with the front end load
mirror not-saturated - bandwidth tends to drop as DC gain goes
up (an artifact primarily of the low current needed to stay in
saturation).
An op amp that depends on the high (ideal) Rout of all the FETs
in few stages, is most likely to disappoint in its AVOL. Simple is
nice, but often depends on perfection too much.