SO I was wondering if there's any point in using a cleaning fluid like Audio Intelligent which purports being useable as a hand cleaning (i.e. no vacuum) solution, or will the crud just stay on the record, just maybe move places?
Exactly right. Dissolving or emulsifying groove-crud (which AI fluids do really well IME) without removing the dirty liquid from the grooves is likely to do as much harm as good. If the liquid evaporates the crud goes right back where it started, though possibly broken down into smaller particles and distributed more evenly.
This may make the crud less audible in lower resolution systems, and that may satisfy some so it's a personal decision. But if there's any chance you'll one day move to a higher resolution system then vacuum removal is essential.
It doesn't have to be expensive, as already noted. A modded $25 Shop Vac works better than nothing. But deciding not to vacuum puts your vinyl at increased risk of permanent damage. Let's not forget, we're dragging a diamond knife through a plastic groove. Any loose particulates trapped between them may damage the vinyl. Whether that damage is audible depends on the system and ears, but if there's crud present then damage is more likely than if the groove is clean.
Having ruined enough LP's by playing them without cleaning, my choice was never to do that again.