In the heat of the summer, I often use a Ken Null inverted rig, his SMZ, with a J frame under an open, un-tucked button front sport shirt. The rig is over a T shirt (with pocket) and the harness is adjusted to hold the gun just to the outside of the pocket (not in the arm pit). My tobacco pouch, in the T shirt pocket, and the usual junk in the outer shirt pocket, covers any print in that area. When the "Y" of the harness is adjusted correctly on your shoulder, it doesn't print through the shirt shoulder or back.
I've been trying to convert this to use with a polo shirt, since reading your post. As others have said, the shirt will have to be loose and baggy. The fabrics used in most polos are not as forgiving as the harder weaves available in the button front shirts. They tend to "cling" more, and complicate things by wanting outline anything they rest on, like the gun muzzle sticking up alongside your pocket. Lots of stuff in the pocket might help, but less than with a harder fabric. Also, the polo shirt and the T shirt fabric will want to cling to each other, which doesn't help. Then, in my area, at least, it is odd to see an undershirt of any kind worn uder a polo because they become heat traps. An open, untucked shirt will vent the heat away better. On the plus side, the inverted rig will draw fairly quickly, if the shirt is big enough to allow you to get most of your forearm inside,and get grip access. The SMZ releases the gun with a twist, and is quick to learn. His SKR, on the same harness, is closed with a pull-through snap and would be even better for this sort of draw. Both rigs are polymer, and impervious to sweat.It could work, if you can put up with the extra layer of shirt material (in 85° temp and 85% humidity) and find a presentable shirt (that looks OK while being baggy on you). The more I think about it, the more I think I'll stick to the open-front shirts, but to each his own. You may be in a position where you are required to look neat, and not overly unkempt. I'm old, and no matter how I look, no one particularly gives a rodents posterior, so I wear what works.