once updated do they stay updated forever
No guarantees but there is a very good chance the answer is yes, when a GPS is turned on for the very first time it has a much harder job to get a satellite 'fix' than it does when turned on after only a few hours of working, this is because it stores info. from the last good 'fix' which can be used next time it is powered on, the list of things it stores include :- Almanac (a database of roughly where the satellites are in the sky which is good for 2 - 3 months), Location (only useful if the GPS hasn't moved too far since last 'fix', Time / Date (Used with almanac to re-create a picture of which satellites to look out for.
All the above data (and more) is stored in something called NVM or Non Volatile Memory this is memory that is maintained when the unit is powered off but can be updated when necessary like the modern microSD card in your cell phone, however this kind of 'flash' memory is relatively new and was either unavailable or very expensive back when GPS started, back then the NVM was kept going by a small backup battery permanently fixed inside the unit
I don't think the 35 HVS has a battery backed NVM but it may have a very small 'flash' memory, so as long as you can power off the unit for say a few days and it still remembers it is in 2020 rather than 2000 or 1980 then it should be OK.
could I just load the final configuration that is still on my laptop
Yes, But I don't think you need to, When you connect another 35 HVS to your laptop running SNSRCFG for the first time It doesn't have a good configuration file, so it is starting from scratch (this is where some older units struggle to get that first 'fix'), however once it gets it's first fix, it has a good config. file so it has no need for the config. file from your laptop, all it needs is the correct date.
I think the only steps from the setup procedure it requires are 17 and 18, 17 copies the good config. from the 35 HVS to the Laptop and 18 sends exactly the same config. back to the 35 HVS
BUT with one big difference, it also sends the time from the laptop's clock including the date to the 35 HVS, so 17 followed by 18 is probably all that is required, I think you may only need :-
1 - 4 setup
11 Check Date in NMEA for $GPRMC having time position date (Wait until you have this data)
17 get good config data from 35 HVS
18 send good config back to 35HVS with time from computer
11 re-check NMEA for $GPRMC having time position correct date
16 power cycle GPS receiver, repeat steps 1 - 4,
11 re-check NMEA for $GPRMC having time position correct date
Notes :-
1) It would be good to take a picture of the NMEA screen before doing an 18 to see what the old date was on one unit
2) I left out step 9 (Use Config/Sensor Configuration) in the original procedure because it resets NVM which is risky if you can make it work without doing so