I don't know about marrow, but squash for the most part needs 'help' to be pollinated if it's not accessible to bees. A soft paintbrush will work (make sure you know the difference between male/female, varieties will have specifically sexed flowers), and you need to work the pollination several times a week, if not every day.
I've been looking into greenhouse/aquaponics, which has similar limitations, so...yeah, you do want to help your plants along to ensure good production. As long as you don't overwhelm yourself with plants, though, you shouldn't have a problem with it, and it can be quite soothing/therapeutic
There are some varieties that apparently don't require pollination, if you'd rather not deal with it, but most of what you'll find in the stores will.