Yes, if the electrical system is not supplying enough voltage, solenoids and relays won't operate properly. Honk your horn. If the electrical system is too weak to make the horn sound normal (ie loud as heck), then it can be too weak to open solenoids.
BTW, I think all Jeep and Dodge 5.9L's came with the 150 amp alternator as original equipment. I think you'll want to spend the little extra $ over the 90 amp and 136 amp prices when you replace yours.