I agree with the rest that offering to work for free is not good .. and you will be severely disadvantaged when it comes to the interview as there will likely be rated pilots looking for the same job.
That isn't my experience. People I knew who either paid for commercial flying or for flew for free raced through the industry pretty quickly and were in QF or Regionals or good paying GA jobs faster than anybody else. It's all well and good to take the moral high ground on this issue, but those who did it in the past seemed to benefit pretty well from it. I have never actually heard of anyone being blackballed but certainly knew of 3 operators who threatened it but noone ever followed through.
The reason for this is that essentially Aviation Recruitment at EVERY level is fundamentally a box ticking exercise. If you don't have the minimum requirements (whatever they are) you will never be able to go anywhere regardless of how many 'hard yards' you've done. The guy with 250 hours ME Command for free is always going to beat the GA hero who has been all around the NT and FNQ but zero twin time no matter what a good bloke he is. That's just how it is unfortunately. I met or worked with at least 5 guys that I can remember in my GA days who had flown alot of twin hours either privately or for free, and everyone bitched about them but they were the guys who got the job because they had the hours in the logbook.