Of course, otherwise the drag would never have let it get hypersonic.
X-15 A2 used the tanks for 55 seconds, then dropped the tanks and used internal fuel for another 90 seconds.
https://www.astronautix.com/x/x-15a-2.html
I have seen footage of the tanks being dropped. Tried to find video but no luck. But I did find this:
Wow, apparently they did a sort of "restoration" of X-15 A2, and added drop tanks to it, at the USAF Museum in Dayton. I do not recall it looking that good when I saw it there many many years ago, with no tanks. So this is not old footage, it is recent:
[video=youtube;_H2he0UUXW4]https://www.youtube.com/watch?v=_H2he0UUXW4[/video]