I've just done a little experiment with Ancestry
I entered a birthdate of 1st Jan 1720/1 and I got a message saying
!There are too many possible values for day. Are you sure?
With a "Yes, use this" link to c lick underneath
I entered the same birthdate but with year as 1720/21 (i'e with the 2 of 21) and I got the message
!There is more than one possible year value. Are you sure?
again a link with "Yes, use this"
So it is recognising a difference in the two forms and it may accept the second version "1720/21"
However if you enter a date after 1751 in this way, the messages are the same as pre-1751 dates, it doesn't seem to recognise a cut off date like FTM does.
There do seem to be a few hurdles to making it accept the dates, particularly if they are added through a later edit and the double year doesn't show up on the time line but if you click view details the double date is still there.
I have managed to make it accept an infant who was born on 1st December 1745 and died on 1st Feb 1745/46 (two months later) without telling me the death date is before birth date.
To see whether the information interchanges between FTM and Ancestry correctly, you would probably have to set up a small test tree and experiment with it. You can have several separate trees on Ancestry.