well, first off, there is easier way to do it if you just want to move the game.
view -> settings -> downloads
click on steam library folders
add new folder on target drive.
(or install any new game and create it at that point)
select properties in arma3
local files tab has now new button, "move install folder" which gives you option to change the steam library folder game is installed to.
select one on SSD drive, wait for move to be over, profit.
edit:
If you reinstall it on top of already existing files, then yes, Steam should find the files already there and skip the downloads.
so if you copy steamapps/common/arma3 to new steam library folder, it should skip downloads for the new install.
but only IF said copy was done before...