Of course, you would have access to most OW lounges with your current BA status, just not First Class lounges in the network. If there's a First Class lounge somewhere, there's a Business Class lounge as well, so it's not like you'd be too bad off (except in the US, I guess).

As far as desk agents believing me when I had virtual proof of enrollment, I found most to be understanding given my (politely) explained situation. Some wanted a card, others just a number, but in the end they were all able to look up my FF account and verify what I told them. YMMV