What happens if the mechanic installs a new chain and rear cassette and the chain links are not properly measured? What effect does that have, either way...too many links or not enough given the rear cassette configuration.

Then what does the mechanic do to adjust for this without trying to add or remove links?

Adding or removing chain links is almost the easiest thing a mechanic can do. It doesn't hurt the integrity of the chain in the slightest. If he is a mechanic he will put the right length in to start with but can change it. The easiest way to do it is he will just count the number of links in the old chain. If it is a new install with no old chain there are several ways to figure the length that are again simple to know how to do. They all work about the same. If you are doing a fixie without a horizontal drop out bike it may not be possible to do it. Roger

Chain length matters.

If your chain is too short, and you ever try to shift into the big/big combination, it can cause serious damage to your bike.
If your chain is too short, and you shift into the little/little combination, the chain will go slack on the return run.

Unless I'm POSITIVE the old chain was the correct length, I always resize a new chain. It only takes a minute or two.
1. Wrap the new chain around the biggest front chainring and biggest rear cog bypassing the derailleur.
2. Figure the shortest place you could rejoin the chain (hint: there's wide and narrow links).
3. Add one inch of chain (2 links or 1 narrow link and 1 master link.
That will yield the shortest chain that will work with your gear combination and the length of the derailleur cage doesn't matter.

Here's an article with photos which describes Retro Grouch's method: https://sheldonbrown.com/derailer-adjustment.html#chain
I always join the chain with a master links; I do not like the Shimano "special joining pin" concept.

I'd also suggest carrying an extra master link and the links remaining after shortening your chain for doing repairs. If you should need to lengthen the chain in the future (like if you install a bigger chain ring) you can use a second master link with no problem.

I'll usually size a chain first with the longest length that the system will tolerate. Then see how it shifts. Only if there are shifting issues (or pulley knock that won't adjust out) will I remove links, and end up with a chain length towards the shortest that the system will handle. I do this so I don't have to add links and suffer the chain with second connecting devices (be they pins or connecting links). Additionally this allows for in the field chain repairs requiring link removals and have the chance of not ending up with too short a chain. Andy.

I believe this is what you intended to write.

Oops, you're right.