Hi Persistent:
In my opinion, it's never a good idea to caulk over grout...new or old.
I have remodeled enough bathrooms over the years that I learned one thing in particular...always best to use a
mildew resistant silicone/caulking between any horizontal to vertical surfaces, i.e., between shower floor and shower walls or between cast iron/steel tub and walls of tub/shower surround
INSTEAD OF GROUTING THESE AREAS to begin with...

(
silicone is much harder to work with).
Why...? Because there is MOLD/mildew behind the grout...even with new installation (over time). That mold always shows through any caulking you may put
OVER grout. It may take 6 months..but it will show up and eventually turn black and yucky!! Then you have compounded the problem!
I install tile quite often and always take the extra time to install a bead of MATCHING COLORED (same color as grout used) mildew resistant silicone/caulking between horizontal to vertical surfaces (
have to let dry 24 hours before grouting...may be why few contractors do it??)....I don't worry as much on the vertical to vertical corners...but some will even put silicone/caulking in these areas.
I would have you remove the old grout (grout removal tools sold at all home supply stores)...then I would have you use isopropyl alcohol to evaporate any remaining water from grout joints (and kill bacteria/mold)...then I would have you use the mildew resistant silicone/caulking I mentioned (available in many different colors today!!)
BUT THAT IS REALLY ONLY IF YOU THINK YOU HAVE AN ISSUE...
Most of the time...leaks are not much of an issue/concern with a properly installed shower pan....If previously grouted and no signs of mold then no need to be concerned for now. Just that I prefer caulking to begin with...and have never seen mold/mildew develop 10 years later (since they developed/popularized mildew resistant silicone/caulking!!).
If you see mold developing...or moisture somewhere it shouldn't be then follow above advice! If no real issues then no need to touch it....that make sense??
Let me know what you think here...
MARK