Sailing a dinghy will make you more aware of the interactions of boat, waves, and wind than a keelboat and you could some dinghy sailing for that purpose but it is unlikely to be a big deal in preparing you for extended cruising. What you could do is really pay attention to how your boat feels and experiment with adjusting your sails (eg traveller or outhaul) one thing at a time in consistent conditions to see what effect it has on boat speed, heeling, general feel of the boat - approach this very systematically and keep notes.
Don't know the curriculum of the courses in the US, others may comment on this. One other way to improve is to crew for people who are knowledgeable - for example, crew on a trip to or from Bermuda to get some offshore experience. Different skippers, different boats, lots to learn and you will get different takes on how to approach the whole experience - again keep notes.
Heading back to Lake Ontario for this summer. Relatively few stops along the way from Grenada. Martinique, Guadeloupe, St. Martin (must have something to do with the French food), then Bermuda, New England and up the Hudson/Erie Canal. We were going to go via Newfoundland and Labrador but June remembered that one of the kids is getting married this summer - details, details!