I'm not great with time, so finding time to train while under the insane time demands of grad school was really tough for me. I was able to manage 4-5 hours in a good week. Now I'm seeking jobs and have all the time I want, but my sanity and general capacity has allowed ~10 hour weeks for the most part. As I adapt to greater volume, maybe 15 hour weeks in base will be possible someday (but it is necessary and important to balance the bike stuff with relationship stuff, and long base weeks and lots of race weekends test that balance!). Fortunately: a relatively small increase in training volume can make a big difference. When I finished my thesis at the end of July last year, I upped my riding to 6-8 hour weeks and went from nowheresville to being able to race competitively in Cat 4 crits within a few weeks, a few months later I was able to ride well in Gran Fondo events and was very competitive in the local cyclocross scene.

Anyway, relevant to the OP: a lot can be done with limited time, but if endurance base is a weakness (for new racers, it usually is), it's a lot harder to work on that with really limited training hours. Luckily, it's possible to do okay in crits on limited training. Road races are harder, unless you're talented. Look around the Internet for training plans and tips for time-limited racers, as I said it will be harder to get the base you need but it's better than noodling around without a plan.