I modified one of my older planes (video below) and proved this possible. Too bad I didn't make a video of it.
Video of unmodified plane:
I put heat shields on the sides, front, wings, etc... In positions where they don't add too much drag to withstand the heat that comes with speed that is achieved and bypassed with the extra whiplashes under the heat shields.
The highest speed achieved was 41,232 m\s, which was achieved shortly after engine flameout before it stopped accelerating during the force glide on prograde.
A few heat shields and wing parts were lost due to the heat.
But a full orbit was achieved.