I wouldn’t worry about downloading your driver card.
When you say “will they see the couple of missed downloads and put 2 and 2 together?” I’m not sure whether you’re talking about an employer or the DVLA, either way it doesn’t really matter because you’re not in a position to get your card downloaded.
-Not that it really matters but you won’t have missed two downloads anyway, your card needs to be downloaded 28 days from the day after the last time it was used, you’re not going to be using your card while in isolation so you can only miss one download.
Having said that, if it’s the DVLA you’re concerned about you can forget it, you have a solid reason for not making your card available for download so they won’t care that it hasn’t been downloaded.