Doing both a full time and a summer?

Hey friends! I have done a SA and signed S&T full time return offer with one of the BBs at London. However, coming from the STEM background, that is my only financial experience. Thus, I am thinking about broaden my finance experience and apply to another SA in a different business area to explore (IBD, Equity Research). In London, many companies accept final year students into SA program. Thus, I can finish off my summer and go to the full time in September in the same year. However, one problem is that if I get accepted into the SA eventually, there is a background check. They will call previous employers, which of course include my full time company since I got the return offer from them. Although my intention is only to learn and explore different business areas, will this reflect badly on me for my full time employer? Will they think that I am not loyal to the company? What should I do in this case? Should I communicate with my full time HR before I start to make SA applications? Any opinion is much appreciated! Thanks a lot guys.