Create a toolbar button with a label that includes &G/&g.
Activate the Windows setting "Underline access keys when available", so the mnemonics of your toolbar buttons are always underlined. (Or, for the sake of simple reproduction, just press Alt to see the mnemonics.)
When pressing Alt+G, the up-arrow icon button to the left of the location bar behaves as if it was clicked with the secondary mouse button, invalidating you own toolbar button with the g mnemonic.
When pressing Alt+A (the default "Admin" toolbar button has an "A" mnemonic), the favorites icon button to the left of the location bar behaves as if it was clicked, invalidating the default visible a-mnemonic.
You can only see the icon buttons' mnemonics when going into customization mode, editing the button and looking for & in the label. This can be irritating and one may think of it as an unchangeable built-in hotkey.
The icon buttons' tooltips won't tell you.
The key search in the customization dialog doesn't yield any results.
I think a mnemonic shouldn't be able to invalidate another mnemonic. In Windows shell context menus, e.g., pressing a mnemonic that was assigned more than once doesn't exucute one entry right away, but let's you traverse through them. You have to press Enter to activate the respective entry.
Also, the tooltips of the icon buttons should underline the respective characters, at least when said Windows accessibility setting is active. But since, without it, just pressing Alt also doesn't provide any means to see the mnemonic, the underlining should probably be there for all, regardless of accessibility settings.
That isn't the case here or in the current default toolbars, at least. The default Admin button has a hotkey (Ctrl+Shift+A) but doesn't have an accelerator.
I think you shouldn't assign conflicting accelerators when editing your toolbars.
Windows hides mnemonics by default, unless the menu is accessed via the keyboard, because mnemonics are deemed to complicated for ordinary users to comprehend.
That doesn't underline the access keys in icon-only button tooltips, only in labels that are permanently visible (or in drop-down lists). I talked about that in my initial comment.
Even if you don't want to allow the user to traverse through elements with the same access key, it still should be more desirable to activate the first element in reading direction with the access key. Reading direction means:
