I've flown in plain clothes as well, once while ferrying, the other time I was called from a standby before my standby even begun. I was in a shop, fetching groceries when the dispatch called. Apparently they called somebody before, an hour went by, something happened to this guy so the ops were running out of time and options.
License not being on your person is not a problem. If you get a ramp check and don't have it on you, the ops have a copy of it and can email it to whoever is interested to see it. A much more important piece of kit is the crew member certificate/and/or any proxy cards you might need to pass through security.