There isn't a clear yes or no to this. The point about invasive species is a really good one. As divers we should be concerned with it and rinsing you gear is important to not spread them. Of course, if your gear sits in your garage for a while most likely whatever you might have would be dead and shriveled up, but maybe not.
Also, how sure are you that the lake water is that pure? Their could be plenty of things in the water that will reduce the lifetime and functioning of your gear. Things that are hard to measure such as fine sedimentation silt or chemicals, nutrients, metals.
Either way you should probably start treating your scuba equipment like underwater life support equipment, not scuba 'gear'. Who knows what might happen to it on its own in the garage.
The o-ring in between your tank and regulator first stage will function better if it is not left under constant compression by leaving things connected. It can deform over time when left in one position under compression and be less likely to keep is 'o' shape. That goes for a number of other o-rings in your setup that, if you are leaving them under pressure, get pushed or smushed into gaps to create the seals that make all your gear work properly.
Sometimes small leaks develop in your gear and all the air could leak out of you tank leaving it open to moisture, corrosion, and failure (assuming you are leaving the valve open as well).
Garages are generally full of lots of bad chemicals and solvents that don't mix well with scuba gear.You might accidentally get them on your gear. Also, I do a lot of work in my garage and wouldn't want fine dust/sawdust, etc getting onto/into my gear.
That being said, dive equipment is built well and will likely function even under the added stresses you are subjecting it to.
Personally, I would give it a quick rinse and hang it up somewhere. It's a good practice to treat your equipment as best you can. Probably will save you money in the long run. I doubt you would ever have a problem with your gear the way you treat it but that isn't the mentality we should take toward our equipment. We should assume their will be a problem with it and do our best to minimize that chance within reason. With respect, I think you could be doing maybe a bit more for your equipment then leaving it in the garage like you described.