Hi, I learnt Level 1 earlier in the year and I'm currently studying towards level 2. I am right handed but wanted to teach some BSL to a friend of mine who is Left Handed so switched the alphabet around quite easily (With the exception of a couple of letters, which I had to think about).
I've also watched other left handed people sign and often forget they are signing left handed until it comes to fingerspelling. Although fingerspelling seems a bit part of BSL early on, I have found that the more I progress the less I am actually fingerspelling because you learn signs for everything. On level 2 the only time you use fingerspelling is for names of people, a few places that don't already have their own signs and Brands that don't have their own signs.
I have also seen people sign one handed (I find this hard to follow, but I'm still a beginner), Example of this is when someone has a cup in their non dominant hand so instead of signing directly on each finger, they point/swipe etc in the general direction (I've done it with my own name and it's easy to do but may be difficult to follow)
I am sure there are many people out there with varying obstacles to overcome in order to learn BSL so I would say it was 100% possible to learn
Best thing to do if you are considering starting a course is to have a chat with the Tutor before joining and ask them the best way to go about it for you specifically
I hope this helps - Good luck with the learning
Esther