OK for dropdown button to be on the left?

Perhaps a minor point, but I thought I'd ask anyway...Normally, the button to drop a dropdown display is to the right of the display area, but I have the option to put it on either side, like so:

Q1: First, the convention is to have these on the right, correct? Why is that?

I thought putting it to the left in my case might make more sense. There will be other controls near the left hand side of this dropdown, and so I thought it would make sense to align the dropdown button there. This will reduce needing to move the cursor further around the display to do common actions. In fact, this applies similarly in another screen of my GUI, in which the left edge is associated most with actions, and so I'd like all dropdowns to have left-aligned buttons.

Q2: So, does this seem reasonable? Or is not breaking the dropdown-button-on-right-right convention more important?

EDIT: I should mention that this dropdown is really a "combo box" that can both drop down a list and also accept user input into the field. For that reason, I cannot have the functionality that the user can click anywhere on the dropdown to drop it, since clicking in the field just sets the cursor there.