Unfortunately, it does not appear so. In fact, when you check the "Accounting Style" button, you may notice that the
$ symbol up in the toolbar actually gets deselected. From Numbers's perspective, accounting style is different from the standard currency style present in the toolbar.
You can, if you like, define your own custom cell style that does what you want. You can see here, I've added an "Accounting" style in the drop down menu:
And my "Accounting" style is defined like this:
Really, though, I don't know that accessing things through the drop-down menu is going to be any more convenient for you than just hitting the "Accounting Style" checkbox.