No it doesn’t. Programs are only scheduled when the current time passes by one of the start times. If a program is interrupted (e.g. due to power loss), it won’t resume automatically. If you have frequent power losses, I recommend you to make use of the ‘repeating start time’ feature, which can break down a long running time to smaller sections, so that even if the program is interrupted it will quickly resume. For example, if a program is supposed to run for 30 minutes, you can set it to run 1 minute at a time, but repeat 30 times every minute. This way the total run time is the same, but it’s more robust to program interruptions.
Another option would be to plug the OS power supply in to an UPS. Even the most basic UPS will run the OS for a few days on just battery power. If you make use of the weather features then plugging your modem and router in to the UPS will give you about 24 hours of run time on just battery. My personal setup is like this and it’s great for keeping the system stable, and it has the side benefit of providing power smoothing to the OS, so power spikes and brownouts don’t cause hard to trace problems.
If your OS is setup in a box outside there are even UPS devices meant to be rack mounted or fit in to the Orbit style boxes. I honestly recommend it even if you don’t have power issues. The small cost does a lot to protect your devices, as even in the best areas power from the wall fluctuates and can cause problems for micro controllers that could lead to premature failure.