Yes, a Fleet Mineral Oil enema will 'soften things up' but within limits.
These are best given, warmed to a couple of degrees above body temperature so as to minimize the urge to poo immediately. Ideally, the enema should be given with the recipient in the knee-chest position because gravity will help the oil go as high as possible in the recipient, and that position should be retained for a few minutes after injection, but that is hard. It's also hard to squeeze the enema in without a helper. The left lying position works pretty well as an alternative.
The predominant feeling with these enema is not an immediate urge to poo, but it often feels like you need to fart. Don't be fooled. If you do release a 'fart', odds are you'll expel stinky oil.
These enema should be taken last thing before you go to sleep while you're lying in bed. If you get up, odds are yoiu'll leak oil. The bed should be protected with a pad or you can wear a diaper. If taken as describes, they usually stay in completely overnight.
In the morning, don't expect an urge to poo. You probably won't feel one. The mineral oil does a couple of things: it somewhat softens the poo and it makes the colon very slippery. The softening will not be dramatic. Hard poo won't be turned to slush, but more like mashed potatoes. The lubrication will make even hard poo slip out, usually without straining. As the poo comes out it will usually sweep out most of the oil.