Not really, though some distros are more secure than others it generally comes down to what software you run (do they have vulnerabilities that could be exploited) and how it's set up. There are some which come better preconfigured as far as security and stability go or perhaps they have tools to ease the configuration, but in general the security depends on how you set the system up. Having said that, it would make more sense to use a distro that by default ships with stable, safe and thoroughly tested software like Debian or CentOS (essentially a free Red Hat clone) and is reasonably well configured out of box. Distros like Arch or Fedora which by default aim to have cutting edge software aren't the safest bet simply because of the risks involved in using software that's had little testing, and in case of the former it's theoretically possible to get malicious packages from the repos as a result of a well-executed attack since they don't do any package singing AFAIK.