If not, is there any reason to keep the wallet file on the offline computer at all? (It seems safest
to delete electrum entirely if the coins are going into deep cold storage, and just have a watch-only
wallet from online computer along with the seed memorized/stored safely.
Not to be rude to the great dev team here, but this happened to me TODAY. It turned out to be a bug in 1.9.6, when I loaded the unsigned transaction on my offline Tails Electrum - it couldn't find the address and failed silently.
Fixed by an update - but it was a little scary!
In older versions you had to nudge electrum to generate addresses beyond the gap limit. I can understand how it might be scary, though.