Will I have problems from waiting to grout patio tiles

I wouldn't be too concerned unless there's mortar that is raised above the level of the grout - which you've already said there isn't.

Scraping the higher sections to give a reasonable depth of grout would be as far as I'd go.

A lot of adhesives these days are sold as tile cement and grout, though they do tend to be coarser than "pure" grout, so they are basically the same material. However, a pure grout does give a smoother, "cleaner" line.

Floor tile grout also tends to be coarser - I suspect to be able to cope with the higher degree of wear and tear it will receive compared to wall tile grout.

It sure looks like you did a beautiful job on your shower, be a crying shame to see all that hard work ruined with stained grout. The glazing agent in the grout needs 8 to 10 days to harden completely. I suggest that you tape up some poly to protect the new grout if you really need to use the shower before the prescribed cure time. A few days of inconvenience is definitely worth not having to scrub and look at stained grout for years to come.