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Is it possible to view games made for Tandy Graphics (TGA, etc) on an IBM 5153 color display connected to an original Tandy 1000 (or 1000/A) in 16 colors?

The Tandy 1000 CGA output was essentially like the IBM CGA electrically, and graphics modes were compatible. There was, however, an important difference in text mode. In text mode, the CGA used the middle 200 scan lines of a 262-line frame to display 25 rows of 8 scan lines each, with generous borders on the top and bottom. Using 8 lines per character meant that the bottom row of letters like "g" and "y" would touch the top row of letters like "E" and "T", which was less than ideal for legibility.

The Tandy 1000 shrinks the top and bottom borders by roughly 12-13 pixels, allowing the text portion of the screen to be expanded from 200 lines to 225 (9 scan lines per row). This substantially improves legibility on screens whose "vertical height" adjustment was set to leave at least 15 or so lines of border visible on the top and bottom. On screens which are adjusted to crop the border more closely to the text, the top and bottom of the Tandy text screen will get cut off.

I don't recall if the Tandy provided any way to use an 8-dot high font, but I wouldn't be surprised if it didn't. The "extra" line was added above the row of text, which meant that an inverse-video "E" would show one line of background above the text and one line below. That would also, however, mean that programming the CRT controller to use 8 dots instead of 9 would cause the bottom scan line of characters like "g" and "y" to be cut off entirely. Avoiding that would have required having a character set ROM which contained two character sets, and would also have required including a means of switching between them.

Basically yes. TGA (1000EX or similar) signal output (colour/intensity and sync signals) and connector pinout is upward compatible to CGA, thus compatible with CGA monitors. Both produce the very same RGBI signal using the same timing and encoding. TGA just employs more memory, thus being able to supply more colours at higher resolutions.

After all, TGA is basically a CGA with double the memory (32 KiB) and modes resulting from that - much like the IBM PCjr, which the Tandy 1000 was set against. The TGA II (Tandy 1000 SL/TL/RL and later) doubled that again to 64 KiB, finally enabling 640x200 in full 16 colours.

At least as long as colour mode is used. Text mode, when used in monochrome setup, is not. The monochrome setting is unique to TGA. Here a single B&W output signal is provided on pin 7, unused by CGA.