Negative, Ghost Rider. EVSE's need a dedicated branch circuit
A branch circuit is defined as the stuff past the last breaker.
So extend the 30A circuit down to a subpanel. The subpanel has two 30A breakers. You must pinkie-swear not to turn both on at once. A physical interlock is not required. The breaker, which is rated SWD, entirely replaces the stupidly inaccessible switch.
So, I would run EMT metal conduit (a new craft to learn, but it handles ground for you) and 1/2" pipe will suffice. Easy to work with once you get the hang of it. And before you get the hang of it, it is trivial to undo/redo, it comes apart like an Erector Set. EMT conduit also satisfies the "protected from physical damage" requirements for wiring in garages. Now you don't have to bust out drywall.
A suitable location for a panel is somewhere it's not likely to be cluttered up with junk in the 30"x36" working space in front of the panel.
Inside the panel, install an accessory ground bar, and remove the green screw on the neutral bar, to un-bond it. That will protect you in case some numbnuts tries to put a 120V circuit there (which it can't support).
Cost would be around $25 for the subpanel, $10 each for 2 breakers, and pencil in $30 for the requisite EMT conduit, plus $30? the NEMA 6-30 recep.
With EMT, you simply use THHN wires -- all will be #10. They are available in a variety of colors, and many hardware stores sell it by-the-foot. You need at least 7" coming into a junction box.
Once the EMT conduit is finished, I'd run four #10 wires - red black orange orange. The switch goes away and is replaced with a 4x4 domed cover - you need the cubic inches in that box for 4 splices. Make sure the utility-side and heater-side ground wires are bonded to the box metal. Then the EMT carries ground down to the subpanel.
Red and black go from supply in the former switch box, to the main lugs of the subpanel. The subpanel gets two 30A 2-pole breakers in it.
Orange and orange go from the 2 hot wires going into the heater, to a 30A breaker in this subpanel. With American 240V with 2 hot wires, nobody cares which wire is which.
From the NEMA 6-30 recep for your EVSE, run a wiring method of your choice (again I like EMT because it carries ground and satisfies physical-damage resistance requirements) to the subpanel, where it lands on the other 30A breaker.