FWIW, my Hawaiian and Mexican wedding shirt collection has grown immensely since Texas passed it's CHL law.
While I cannot speak for others, I'd notice the tab, in-fact anyone frequenting the same restaurant, where I happen to find myself, that's carrying a concealed handgun is something I notice or at least attempt to.
I'm especially fond of strong side or right hip carriers because they are the easiest to spot. Although most folks won't notice, call me anal, but I prefer/attempt to identify any CHL practitioners with which I come in contact as a simple matter of course. It hones the senses to be a practiced observer, and gives me a warm and fuzzy feeling to pay attention to the details.
As a one-time CHL instructor, I felt it was my responsibility to determine for myself, the aspect of CHL in all manners. So for several months I experimented with all manner of carry modes. From Renegade ankle holsters to Bianci and Galco leather rigs and shoulder holsters, I tried to carry different pistols in different modes. I learned a lot, but mainly learned "what worked for me". While teaching I attempted to answer those questions asked by students about particular modes and styles of CHL and on occasion explained why I use and carry in the mode I do.
From riding in the car/pick-up, or my particular favorite, "scoots", to those trips to the little boys room, how and where ya carry is important. Nuthin is more embarrassing than dropping your trousers only to have your pistola hit the floor, (not to mention the reaction from the dude in the next stall) or am I the only one who ever had to go while in carry mode. What works for me might not work for you, but I always attempted to alter my carry methods at first to be aware of associated advantages or disadvantages of that particular mode of carrying.
If a fanny pack works for ya swell, they are a definite step ahead in the "john" situation, IMO.
Your grips and the material your shirt is made of are definitely something one must consider if "strong-side/hip" carry is your choice as pistol is somewhat out of your peripheral view and printing can happen without ya knowing. So making sure that the polyester shirt don't stick to the sharply checkered 1911 grips is a priority.
There's way to many variables to type here and I suggest ya do your own testing to find out what works for ya.
For me, I'm happiest when the fact I'm carrying comes as a complete surprise to everyone around me, at anytime and anyplace, (except where prohibited).
Mike
PS - While last in Cooper's small book on "Principals of Self Defense", never underestimate the value of SURPRISE.