I think it depends on the stage of the startup, and how much of a key employee you are to it. Can they afford to have you away for that long? Do they have a PTO accrual policy? Have you been making use of it? Do you have at least 6 months of savings for bills / rent should you not have a job? Also consider the expenditures you'll have while taking the sabbatical with half the household income.
A strategy I used to do was that I took unpaid PTO when I wanted time off to let the PTO accrue, then took all of it at once when it maxed out (when that happened, I was on PTO for a month and half) after finishing a major project that took a year to complete. The PTO would also increase in value as I got raises over time.
The company wised up and stopped letting people do unpaid PTO if you had PTO to use because of me.
Even if it's unpaid leave, they still have to pay for your benefits while you're away I think.
Going on the face value of what your original post says, it sounds like a very risky thing to do. PMs are going to have a significantly more difficult time getting a job than an engineer I think.