But if they got married in the US, and she doesn't have a settlement application currently under review, how would the IO know or suspect that she's trying to screw the system and overstay a visa? She should have the normal stuff we'd all bring along to prove we're only on holiday (i.e. rental/mortgage paperwork, a note from work, return ticket, etc.) but I figured that was just assumed. His question was more could she fill out the online portion in the UK, which she totally can as long as she goes back to the US to finish the application process.
The IO will have no proof she's married to a Brit, nor that she's intending to fill out an application for a settlement visa. She'll be going to the UK on holiday, and then going back to the US, simple as that. She definitely can't travel while the visa is being processed, but I wouldn't think she'd get any extra hassle if she goes *before* she applies.
Edit: especially since she's only visiting for a week. If it was for a few months or whatever I would be more reserved, but if she has a return ticket, and maybe a job to return to or a house she's responsible for to show to the IO, I doubt they'll question her any more than they'd question anybody else trying to get into the UK for a holiday.