Yes, I'm sure. You couldn't shift out of park otherwise since you need line pressure to engage the clutches. You'd disengage the parking pawl but that's all you'd get -- ever.
The pump is driven off the input shaft on every ATX I've ever seen, even the very old mechanical ones with a vacuum modulator for shift point modification (which was how they used to work before electronics came into the game.)
Solenoids are rarely an issue. What IS frequently an issue is that the pistons in the valve body are typically steel and the body itself is aluminum. Guess which one wears preferentially to the other? Uh huh.... Then line pressure goes down due to leakage past the pistons and if that goes far enough the clutches start to slip. Once that occurs you're done and the gearbox will be severely damaged within a few thousand miles -- if it doesn't fail outright.
If a solenoid actually fails then yes it obviously needs replaced but they rarely do. Be careful playing with those unnecessarily; the connectors frequently get brittle with time and heat and if you break the locking tab on one you're in a lot of trouble in terms of the work required to replace the connector or harness.
OE fluid in modern ATXs is typically fully synthetic and of good quality, just as with modern 0w20 engine oils. The proof that 0w20 is perfectly fine is found in UOAs, which I've posted on the other thread (and elsewhere on the site before); spectrometers don't lie.
The issue with ATXs in general, other than the decision to put the clutches in the wetted section where they inevitably MUST shed material into the lubricating fluid, is that they all run the gear oil through the radiator for heat rejection which means the oil typically runs a solid 10-20F hotter than the coolant is, and as load goes up that disparity goes up too. Engine coolant temps have been intentionally run higher over the years for emissions and efficiency reasons so it's not at all uncommon for coolant temps in the ~210F range to be normal; this means the gear oil usually runs in the 230F area which is right on the edge of "ok." Get materially beyond that and dino oils start to break down; synthetics will tolerate a higher temperature but hotter is definitely not better in this case. With older dino-based ATF fluids adding an auxiliary cooler *after* the radiator core one if you drive in summer months and especially where the torque converter is unlocked (which is pretty much all the time in the city and in heavy traffic) will frequently *double* an ATX service life. If you pull the stick on an ATX and the oil has *any* discoloration at all compared to what it looked like coming out of the bottle it's been compromised by excessive heat and both it and the filter should be *immediately* changed. (Not all ATX fluids are red in color these days and on many modern ATXs there is either no "stick" at all or it's a bear to get to it....)
There's a reason trucks with towing packages have an auxiliary transmission cooler on them.
My primary experience with transmissions is the ZF 8 speed unit found in BMW's. With those units, after 70K miles sometimes an aggressively driven transmission starts to shift roughly when the unit is really hot (or sometimes really cold) and is more prone to do it in specific gears rather than all 8. A solenoids replacement would make these units feel like new and made even more of a difference than just fluid/filter change alone.
As for valve body, definitely a good idea to rebuild/replace that when you have the pan opened up to replace fluid. I guess the solenoid point does not apply as much for the SKYACTIV transmission.