Really, I don´t think you can conclude back from events after 1981. So far I do not see any reason why in 1977/78 it would matter whether you were a "new team" or not. What obviously did matter was, whether you were a F1CA/FOCA member or not, because it meant that you had some advantages concerning the acceptance from organizers, starting money, travel costs etc., and this probably depended also on your merits from the previous season. But still you could, like ATS in 1977, just buy a car and participate as an independent "privateer" without F1CA/FOCA membership.
Regarding events after 1981, I'll return to the point shortly.
It mattered whether you were a "new team" in 1977/78 because, on my understanding, you couldn't join F1CA unless you had participated in the previous season as a manufacturer and met a minimum performance qualification (a sixth place or higher). In those years, the F1 season started with races in South America, South Africa and the USA; F1CA membership allowed financially poor teams like Ensign to attend those races.
ATS couldn't have been a member in 1977 because they were a team racing a purchased car. As a new manufacturer in 1978, ATS didn't qualify for F1CA membership on their own merit so the team purchased March's seat and benefits. ATS entered two cars at every race except Japan (no entry, explanation anyone?) and scored zero points in the season after a promising start. That results score would have pushed ATS out of FOCA (for the new name now applied) and in 1979 ATS entered a single car, scoring points. In 1980, ATS were back in FOCA and submitted two entries.
For ATS , F1CA/FOCA membership = two cars, and non-membership = one car (with occasional guests). It would be wrong to conclude too much from the behaviour of ATS/Gunter Schmid, but membership was not a minor financial consideration in those days.
***
Who else bought a F1CA membership at the time? Frank Williams Racing Cars became Walter Wolf Racing, but Walter Wolf acquired the entire entity including the factory. Wolf bought more than a piece of paper.
One interesting thing about the ATS/March deal, as uechtel notes, is that March sold some intellectual property and consulting time, bundled with F1CA membership. A few months later, Max Mosley (ex-March) became an employee of F1CA (or was it FOCA yet?), the organisation which had approved the deal which set him free.