Yes it does, subject to all the caveats you've been given.
You are a very fortunate individual. You have a paid job flying SE turbines that will allow you to build your CV. You have an employer who is happy to have you gain experience in twins, and if you continue to get paid then sooner or later you'll be able to afford a rating.
The issue is what does the client think you can do, and what would you tell your authority if you were ramp checked ?
At least one reputable operator I know in the UK faces this problem from the other way round. A broker might ask for their own representative to be on the flight who is probably known to the client, but may or may not be a qualified pilot on type, and who doesn't meet the recurring training, checking and currency requirements to fly as commander. They get the 'representative' and the broker to sign a waiver explaining that the 'representative' is just another passenger.
At the very least, you need to have a full and frank discussion with your employer. If they have a problem (shortage of qualified pilots) and you can be part of the solution, then as Thracian says why not try and find a solution that allows you to do it properly. Just make sure that you know what 'properly' means.