They've given you no deal flow and it sounds like you may be suitable. Do it. Moreover, in the worst case (that you're rejected) that does not need to mean you are not good for other engagements with them. Indeed, you may well impress at the interview, but just miss getting the job. That'd wouldn't count negatively.
In terms of professionalism - most firms worth their salt always treat job apps in a confidential manner, so I wouldn't worry about it getting back to your bosses.
Tutoring for early-stage investment banking and consulting interviews in the UK: