Yes, you can do that with 2 different menus on the same page. You will just have to set the current setting for both of them.
The way the menu checks if it is on the current page is t that it compares the current url with the one that it links to and if it matches then it will be marked as current, so 2 different menus that both link to the same page will both be marked as current if they both link to the same page. Similarly, if you have 2 menu items in the same menu that link to the same page, they will also both be marked as current.