If I were on full pay for the duration, yes. But DP would have to keep quiet, because his contracted hours are made up by working over and above, both there and in other jobs.
Trouble is, I deal with sick kids every day. During the November-December flu/tonsillitis/norovirus outbreak, I was dealing with up to 50 kids a day. If that is replicated by covid19, or if even one were to be diagnosed with it a fortnight, I'd be permanently in isolation, as would everybody who stepped in to cover me. If it is unpaid, I'd have to hope that I don't have it and don't spread it.
I think that it's more likely that schools will be closed as soon as they run out of support staff/first aiders.
I'm wondering how it will work for universal credit, though. If you're not being paid, can you submit a claim? And if you do, are you automatically exempt from a) going in to sort it/ID meetings/commitment meetings/ signing on, b) jobseeking activity, c) will they accept your word for it, or will they only accept a doctor's note (when you can't go to the GP) or a positive test for it?
Can you imagine the sanctions being applied and the poverty caused by that - or the level of spread from job centres?
I can't see them exempting everybody, including those who have never claimed before and paying without a fuss. So if it is that widespread, I think it'll have to be allowed to do its worst. Because people need money.