Been there, done that, got the T-shirt.
I am one of those who did what you say. At 450 hours, I got my FE ticket from a program at Carnival - "you get it and we might hire you". They were furloughing by the time I finished so no job there. This was back at the end of '97. I did get hired by a Part 121 supplemental carrier that was looking for mechanics or pilots with low time that they could put in the FE seat for some stability. They had been playing the musical seat game and losing a lot of money on training.
After building time on the side - I bought my own airplane - I upgraded and if the company was still in business, I would be a captain now. Instead I am waiting for a class date on the CRJ with a company which appears far more stable.
Would I do it again? Sure. Do I think it is a reasonable career path? No. There aren't as many carriers out there that a low time pilot/FE could get on with and the ones that are there can be selective with the number of candidates out there.
I mean, I have hit on virtually everyone who flies 727s and got no interest with 1500FE, 1100SIC, 2200 total and Part 121 current and qualified. Why should a company go with a low time pilot who is totally unproven with what is available in the market?