They don't have to be level, they have to look straight. This can actually get quite complicated when doing tile or vinyl planking (especially those with no underlayment).
If you have "rooms" and the basement broken up a bit this shouldn't be a big issue. Try to get trim in one piece for each wall - if it isn't then set each wall and take a look before nailing. You want the top to be straight and not pressing the trim on the floor to make it angled. Not only will this look bad but it wont meet corners right.
There are time where you will just live with a pretty big gap on the bottom on certain runs - can be a good 1/4". Then you can decide on if it looks ok or if you need to put down quarter round or something comparable.
If you think you are going to rip the boards at a slight angle or even plane them... well I am sure it is doable but you are in for a logistics nightmare and tons of work for possibly something that looks worse.
I for one just leave the gaps - as-is - on the bottoms. I see it, yes I see the gap but no one else ever notices and it looks cleaner than quarter round or shaving. That is unless you are lying on the floor look at the gaps.
If you lay it out and the gap is not acceptable a work-around would be a nice decorative rectangle trim cap in the middle and start over from there. But with carpet you have a ton of play - way way more than 3/8". So you should be able to start low on the higher end and go straight across.