In short no, or at least: You should not do that.
Navigation drawers are usually to be used with fragments that you swap, they should not create new activities, since the drawer can not (or should not) be shared.
You should overthink your navigation, and use fragments instead where appropriate. Following the design guidelines, again, navigation drawers should be the top most navigation, and no other activities should have one either.
The answer on how to use a common drawer would hence be to use an activity with the drawer managing different fragments.
If you absolutely must, you can detach the navigation drawer view from the layout, keep the reference some place, then reuse the same view in another activity. This is really dirty and as mentioned, you should not do this.