Too much agreement here, let me stir things up a bit.
Since you can put attachments like slip-sheet attachments on lift trucks that essentially push and pull loads, I have to assume that there is at least some ability for the front end to handle these types of forces (althought the drive systeme isn't necessarily used for this type of pushing).

Also, in practice there is a lot of pushing/nudging going on with lift trucks. Having spent a fair amount of time as a driver, there are times (especially unloading trailers) where you really have no alternative but to nudge a load into a position where you can then properly get under it and lift it. Also, if you watch drivers in any high volume full-pallet environment, you will see that they frequently drive into the pallet until the load hits the backrest. I say "hits" because they basically have a mild collision with the load. Obviously they could slow down and ease into the load, but that's probably not what they are doing in these very busy operations. I have a hard time beleiveing that the lift truck designs are not built to take these forces.
I'm well aware that this is not the lift truck's "intended purpose" and that pretty much any lift truck safety training will say this is a no-no, and would also agree that there is no valid reason to push a load across any significant distance, but in practice, nudges are a reality and lift trucks better be designed to handle the forces that occur when you nudge a load.