Suppose I took a modern GPS receiver back in time to 1985. Would it work with the satellites then in orbit (recognising that accuracy was intentionally degraded)?
It should. The Block I sats transmitted the same L1 and L2 signals that are used today.
Wikipedia says GPS became fully operational in 1995.
There was an issue that the format of the signal transmitted the week number with 10 bits and it caused a problem with some receivers when it first rolled over in 1999. I believe the number of bits for the week has been increased since then.
Still, I have a pretty old Garmin receiver which still works pretty well.
It is entirely possible that the GPS receiver software has a “sanity check” that rejects dates before e.g. the year the software was written. If the satellites are telling it that the date is way in the past, the receiver may just conclude that something is malfunctioning and refuse to do positioning.
Planning to put it in a Delorean, are you?
On a more practical note, how do GPS satellites synch with your car’s position at any given instant if their clocks are not in synch? For the longest time, I thought the satellite would have to be moving near the speed of light before this becomes an issue, but only recently I came to read that apparently the change in gravity itself causes a change in time? /mindblown/
Ok, ok! So, I’m still living in a Newtonian world. 
Help me understand!
GPS satellites carry atomic clocks which are kept in sync with a maximum difference of a few nanoseconds. The whole concept of GPS is based on that premise and would not work otherwise.