No. 16 MBs of ESRAM allows for 16 MBs of texture. If that 16 MBs is exactly what you need to texture every pixel on screen, it's enough. If you need more than 16 MBs of tiles to render the screen, you'll need to copy tiles into the ESRAM, which is something of a waste of BW if you aren't going to reuse the tile. If the scene changes, you need to load in more tiles also.
Allocating ESRAM to textures depends on reutilisation. Frame to frame changes could be low enough that it's plausible, although then you have less RAM for everything else and a key point of PRT is reducing BW requirements. So you'd be using up ESRAM space to save a tiddly amount of BW and reduce latency on texturing which is one area GPUs are specifically designed to accommodate high latency. Doesn't make sense to me.
Using PRT for non-texture data (especially stuff you write to as well as read) could make some sense as others suggest, but storing your level textures in there seems pointless to me. Maybe for destruction, like writing bullet holes to textures, keeping the immediate tiles in and drawing on them, and then swapping them out as the player moves, would be worth doing?