There's just one slightly opaque pitfall, not all laptops have a BIOS setting where you can specify what to do on power-loss and power-resume. So the laptop "server" stays off and you need to intervene manually.
Never had power out for long enough that the laptop didn't survive. Automatic shutdown of optional services at 80% battery level might also mean that it survives 2-3x as long, if this sort of thing is likely to hit where you live. Or buy a tiny UPS.
(One of the major advantages of laptops not manufactured in the last 3 years: replacing the battery to make it good as new takes 15 seconds. Click out, click in. They don't make 'em like that anymore :( )
If the battery were to run out: on 355 of the 365 days per year, there will be someone home who can push the button within a few hours.
And if it's one of the 10 other days: email will retry for 24 hours and everything else is somewhat optional for me. I can call someone to get there within a day, or change the DNS records and turn on a VPS to temporarily buffer the incoming SMTP. I considered my contingency options but never got close to needing it.
I've had better luck with thin clients ...