With typical motor topologies Xmax is going to be taken down compared to a deeper sub. Most shallow mount subs are in the 6-9mm range concerning Xmax. However, the thing to keep in mind is that their competition (normal, low-end subs that are shallow-ish) have about the same amount of linear travel. As far as the box requirements, that's all in the design. You can have two shallow subs and have one require 2 ft^3 and another require 0.5^3 and have the same low end extension (2 ft^3 is stretching it a bit, but I'm just giving you an example). Just because it's shallow doesn't always mean that it requires less space than a normal subwoofer.
Clearance-wise, there is plenty of clearance for most sub-500 watt and power applications. With a shallow cone, the proper suspension, and a shallow motor design, you can end up with plenty of travel for the intended application.
What you're not going to get is 4" of travel and 2000 watts of power handling out of a sub that's 3.5" deep. But what you can end up with is a very good performing subwoofer that is 3.5-4" deep off of 200-400 watts.