Hey there, I would not ask for a referral directly. However, mentioning your interest and talking about yourself in this context is ok, as you do need to sell yourself. Ideally though you would need to move the conversation off email to actually have a chance at a referral - either meet for a coffee or do a phone call. Before asking for a referral, it would also be a good idea to first ask for either tips, or if they could review your CV (although a principal is too senior for this, this last advice would apply more if you contacted an AC/Consultant).
I also wouldn't put all my eggs in one basket, and try reach out to others - youre more likely to get a referral from a junior, even though it obviously has less weighting.