A wet vent needs to be bigger then the existing drain line for it to work. Since the washer is a required 2", then no, you could not wet vent the toilet with the washer 2".
Wet venting is limited to vertical drainage piping receiving the discharge from the trap arm of one (1) and two (2) fixture unit fixtures that also serves as a vent not exceeding four (4) fixtures.
Each wet vented section shall not be less then on (1) pipe size exceeding the required minimum waste pipe size of the upper fixture or shall be one (1) pipe size for the sum of the fixture units served by such wet vented section, whichever is larger, bu in no case less then two (2) inches.
Horizontal wet venting is allowed for "bathroom" sets.
No mention of a washing machine being allowed.