So I was running a burp active scan while I still had this proxy enabled, and it reported the following:
GET / HTTP/1.1
Host: 0312i1bkk8obx8ks6zjcxn4uvl1kpcr0hn7bw.burpcollaborator.net
Pragma: no-cache
Cache-Control: no-cache, no-transform
Connection: close
HTTP/1.1 200 OK
server: Burp Collaborator https://burpcollaborator.net/
x-collaborator-version: 4
content-type: text/html
content-length: 60
Date: Mon, 13 Nov 2017 21:18:58 GMT
Connection: close
<html><body>u7rlb1gwv1pfcez5563zzjzjrgkugifigz</body></html>
Knowing it'll happen means I can account for it, but might pose a potential (rather small) risk when proxying through this server.