No, our plan is to take the Heathrow Express from Heathrow into London, thus the need for the railcard before we leave the airport. My next task is to figure out whether I can buy an Oyster Card from a machine, and add a 7-day Travel-card to it, since it appears from Nigel's reply that the manned ticket counter for the underground may no longer exist at Heathrow. The TFL site hints at a Visitors' Centre office at Heathrow that may sell cards, but trying to find that office on Heathrow's online interactive map has been futile so far.
If your only concern at first is getting into London, then maybe having the "Two Together card" right away is not a great concern, just go into London, then get it there for the rest of your travels. Depending on where you are staying, the Heathrow Express may not be the best option, the Underground may be better.
As for an Oyster Card, if you each have a credit card with contactless capability (or Apple Pay/Google Pay on your phone), you can use that just like an Oyster card with no additional effort. Just tap in and tap out (or tap in only on a bus), same benefit as an Oyster card. When I was at Heathrow a few years ago, machines did sell Oyster cards though....or just buy a ticket to get into London.