So, long story short - no, one cannot open a bank account in Vietnam without a 12-month visa at the moment.
Full story:
In every bank they first of all ask how long you stay in Vietnam. If your visa is less than 12 months, then usually it is game over. However, Vietcombank offers special accounts for those with shorter visas. These are severely limited bank accounts, basically akin to digital wallets.
First of all, no plastic card can be attached to them. Not even local ATM card can be issued. No
cash deposits/withdrawals whatsoever. Top up only via internal bank transfers or from overseas. Inward SWIFT works fine, I checked. In theory, outward SWIFT is possible, but guess what - it is not available online, one has to go to a bank branch in person and do some paperwork to initiate a SWIFT (or whatever else) overseas transfer.
Overall, those Vietcombank accounts are OK for long stay tourists who want to pay for services in Vietnam, but for those who live outside Vietnam, these are basically useless at the moment.
If some time in the future Vietcombank added support for online overseas remittance to their mobile app, that would be great though. I keep both my VND and USD accounts for now, athough chances they ever become useful are slim.