The reputation you make for yourself as a FI(R) may well mean that your Head of Training is able to give a strong reference for you to a potential airline employer.
If the airline's recruiter happens to spot the name of the referee and trusts his/her judgement, a quick phone call might make the difference between your being called for interview or being told "Sorry, no thanks".
If you're prepared to work hard as a FI for a couple of years, in the knowledge that you won't be particualrly well paid and that it's something of an apprenticeship, you might have an edge on others. But it's all something of a lottery - unless, as at least 3 of my ex-FIs had, you have something which holds you up above the rest of the herd!
Good luck!