I'm taking Metabolic Biochemistry (BIBC 102) as a concurrent enrollment student this semester, and the whole process has gone very smoothly. Like you, I was worried that there would be no available seats, but the administrative people in the Biology department and at UCSD Extension made it sound very unlikely that I wouldn't get in, and in fact I had no problem at all. Clearly my experience is anecdotal, and it is possible that you could get unlucky, but everyone I spoke to made it sound like getting completely shut out is very rare.
You should make sure, however, that you are talking to these people ahead of time and meeting all applicable deadlines. One good resource is this site:
https://bookstore.ucsd.edu/launch/scheduleofclasses.htm
It lets you know the available classes and times, as well as approximately how full the enrollment is. However, even if the class says it is "full" don't necessarily assume you can't get in. I was told that they administratively hold seats aside for UCSD upperclassmen, to ensure that they have priority, but that by the end of the registration period spots almost always open up.
You will have to deal with a little bit of uncertainty, unfortunately. While my professor signed my concurrent enrollment form after the first class, the biology department policy is to sign it on the Monday of the third week of classes. So until then I was going to lectures with no guarantee that I would get credit for the class, and I had to jump through some hoops to get provisional access to online materials. The positive side of this is that I wasn't asked to pay anything until I was officially enrolled, and all of the administrative people I worked with made the hoop-jumping as painless as possible.
Good luck!