not really, Docker (and similar containerization technologies) provide a restricted environment for the downloaded code to execute in (by default, it is possible for users to remove the restrictions)

Assuming a default Docker engine install, and no options passed as part of the run, an attacker could DoS the box most likely, and may be able to intercept traffic on the Docker bridge network (although that's not a trivial thing to pull off), but they're unlikely (absent an exploitable Linux kernel flaw) to be able to easily compromise the underlying host.