1. Yes, you can do it, but why?
If distance/time is the prime consideration then perhaps you may have to do the WE.
But you can also save a chunk of miles by riding due west
from West Yellowstone, MT thru Stanley, ID to Ontario, OR.
For much of the Northwest, July & early Aug is the very best time of year.
Late spring or early fall is probably the best time for the WE.
2. Be aware that Nevada and California will have extreme fire risk this year.
Many of the campgrounds could be closed by mid-summer to reduce fire danger.
There will likely be fires in Calif because of the extreme drought.
Some of the WE highways could be closed requiring detours because of fire proximity.
I've done both the WE and the Western TA multiple times. (Also the Idaho connector)
Each has its own beauty and plusses/minuses.
All things being equal (which they never are) I'd do the TA in July/Aug.