Robocalls That Are Obviously Scams

Got what I believe was a robocall that wanted to give me zero interest on my credit card.
Then they said enter 1 to talk to a representative. (I sometimes enter the 1 just to call them a rectal orrifice)
This time the voice said I was 12th in line. It quickly dawned of me that this ma have left the connection to my cell phone active, to be safe I turned the cell phone off ---- Question If I had not hung up then would it have been an opening for some bad guy to go wandering thru my cell phone memory?
Another thought - If I hung up but the caller did not, does he still have a connection to MY phone so he can continue with his nefarious planes?

 

I guess I gave too much info, sorry.
The question that needs to be answered is - If I had stayed on the line and waited for the “my turn”, then I believe the line to my phone is open. During that time could a “bad guy” get access to the stuff I have stored on my phone?
Could the number I had called, dounload something to my phone while I was “waiting my turn”?

 

Voice and data are transmitted separately.