Navigate web menus with keyboard on small screen?

I'm tasked with finding accessibility concerns on a webpage. The site has a main menu at the top of the page:

• When the user's screen is wide, all top level menu items are shown in a single row. When the user hovers over the menu items a dropdown shows level 2 items.
• When the user's screen is smaller the menu is collapsed into a "hamburger menu" that the user can fold out. All levels of the menu can be reached by expanding parts of it.

This, I believe, is a quite common pattern for menus these days.

Now to my question:

The main menu cannot be operated using only the keyboard when it is in it's collapsed state, that is when the user has a small screen. Is this an issue?

My first reaction was that this is a serious issue. However, then I realized that this state of the menu will only be shown on mobile devices (right?) since it is only shown when the user has a small screen. Do users of mobile devices ever navigate using a keyboard? On smartphones that's not really an option is it? But maybe users with for example vision impairments connect some peripheral similiar to a keyboard to the smartphone?

I'd be very thankful for any information on this subject. Also links to good resources would be appreciated! :)