Pressure directly from a propane tank is 100-200 psi.
Pressure to a grill via a low pressure regulator is 6 ounces (10.5 inches water column)
Even pressure via a high pressure regulator can be between 1 and 60 psi.
So emphatically NO. You do not want to hook up your gas grill to an unregulated tank.
Even Tim the Toolman wouldn't do that.
But if you want to use your Weber both ways, just do what I did for my Coleman LXE. I have a regulator that I can screw on when using it with bottled propane, and then another attachment without the regulator when running off the low pressure TT quick connect.