You will gain something by regular gymmming but need to work to avoid hypos, to answer both sides of your question?
1) make sure that you don't have "insulin on board" when you are starting to work out
2) depending on how much the workout makes you drop your BG, maybe have some carbs, maybe just 10-15, maybe more, you really have to test this
3) the "numbers" benefits of working out don't always relate directly to diabetes. At the same time, stuff like lower heart rate, lower BP, bigger biceps, etc. can lead to taking less insulin and feeling good, which are very important, given that diabetes can be a drag. I work out a lot (gym in basement, running, I started doing Tae Kwon Do which I also liked a lot, as it had incremental progress and a lot of feedback..."that's good, here's how to make it better...good...now do it 50x" or whatever.
4) it may be annoying but it's very useful, particularly if you're starting a program of some sort, to check like 1/2 way through the hour or every 1/2 hour to get a feel for how it's going. I've always found it easy to run my basal a bit "hot" which, in turn, can turn into lows easily if I work out more or faster or heavier or whatever? The only solution is to test. I find that I can tell when I'm getting low running if I run down to the 70s so I figure the same would apply to weights or anything else? Keep it up though. I didn't start that stuff until I was 37 years old and sort of wish I'd started earlier?