Heck no.
I'm going to ignore the whole "working for free" question for a second, and how you will almost certainly never be compensated.
The issue I take with this is: If you're working for free then stock should be given to you from day #1, not suddenly given to you in a lump sum after a year. The way you describe this, the owner can fire you after 364 days, and you aren't entitled to stock or financial compensation. And frankly, some of the people I've met in the startup world are sociopaths and will happily fire someone after 364 to keep a large % stakehold in their company, then will rationalise it, and sleep like a baby.
Now taking stock over a salary is a bad idea in general as stock in startups rarely pays out. And if you're taking stocks in lieu of salary they should be worth MORE than salary given the levels of risk and the relative values to you (stock is worthless even for years after you receive it). Plus stock's value is subjective anyway, are they going to get a valuation by an independant organisation, or just declare the company's value arbitrarily?
Honestly the whole thing sounds like a great deal for them, and a terrible deal for you.
You better be best buddies with this guy to consider this since trust is key here. If they're taking a salary then run away. I'd also re-negotiate so some stock is given earlier so less lump-summing occurs.