How feasible is it that we could see the Central Black Hole Sgr A* occlude one of it's closely orbiting stars?
I'm sure someone will write a longer/better answer, so I'll keep this short and just mention that when a black hole passes between the observer an a star, we usually say that it becomes gravitationally lensed rather than simply occulted. This can potentially provide much richer data than an occultation but requires more complex analysis. 

Optical/Infrared

It also takes heroic efforts to try to image near Sgr A* optically. You need to use infrared wavelengths because of dust and an array of telescopes using adaptive optics, combined interferometrically. See How did they make a video of the center of the galaxy, and what is it exactly that's flashing there?

If there was a dedicated, second Very Large Telescope array pointed at SgrA* all night every night, there is certainly the possibility that a gravitational microlensing event could occur, and an otherwise invisible star could suddenly brighten substantially as it passed directly behind Sgr A*. 

Are there candidates?

As far as I know there are no currently known stars closely orbiting Sgr A* that are likely to pass directly behind it. However, I suppose that there could be one so dim that it has not yet been observed, and a lensing event would be the first time it gets noticed, so this is certainly a possibility.

But lensing can brighten any background star, it would not have to be in a close orbit around Sgr A* at all. 

Radio

Gravitational microlensing works essentially the same at all electromagnetic wavelengths, so it can be observed in radio as well as it can optically.

However, individual stars tend to radiate most of their energy optically and are not so bright at radio wavelengths. It would be hard to pick out the radio radiation of a background star above the strong emission of heated plasma in SgrA*'s accretion disk.

To this end I have just asked How far have individual stars been seen by radio telescopes?

I think (but I'm not sure) that you'd have to pick a time of extreme quiet (little/no infall) to even try.



above: homemade GIF from ESA video ESOcast 173: First Successful Test of Einstein’s General Relativity Near Supermassive Black Hole