Yes you just have to be careful not to overload it.
If you’re comfortable running ethernet cabling through your walls and attic, why is running an extension cord as well too difficult?
Not that I would recommend operating a switch in a non- climate controlled attic. Far better to just terminate all the ethernet cables in one or two 6-port keystone jacks somewhere inside the house, and mount the switch there.
That switch has a maximum of 46W and a maximum of 25W per port. Calculate what you might need for electricity in the attic and look at the parameters of the poe equipment.
If you’re going to be using all ports eventually, that’s a plus or minus you get 11-12W per port depending on specific devices. The injector is 60W…so your cable will have to handle 60-45W. If it’s a good branded cable, it’s ok, but the cheapest s***, I’d be afraid that the house would burn down. 
Although it would be best to lay an electric wire and make a socket…
Just as sidenote: You can also “reuse” less powerfull PoE injector (if you have a spare from other UniFi products) to power the Flex switch, but then the Flex Switch POE output is limited (on how many devices it can supply and how much power they can draw).
Hmm. That is probably ok. The Flex switch is rated for 55c temps, but I dont believe that is ambient temp as it says “max operating temp”, which to me means the actual temp of the device. Still, if its rare you hit up at 40-50 ambient up there it will probably be fine.