In my experience, it is not necessary to use enzyme to detach macrophages. They detach easily using 2mM EDTA solution and some vigorous shaking of the flask. Afterwards, just permeabilize as usual, no problem at all.

But even if you insist on using enzyme, it should not interfere with your subsequent procotol. Just make sure you wash off the trypsin (or whatever) completely

To add on to Lisa's answer, if you are culturing the macrophages on poly-HEMA-coated flasks/plates (which is what I do), then detaching the macrophages likely wont require enzyme-mediated detachment, as this material limits cell adhesion.

Regardless, intracellular staining post-trypsinization shouldn't be an issue. 

Thank you for your quick answers!