In general, no. Especially if the email group you're using corresponds exactly with the queue assignment in the ticketing system.
However, it depends on the effectiveness of your ticketing system. If tickets routinely get mis-assigned or never-assigned, then emailing the people most likely to address the problem will help speed the process. And if that's the case, they're probably already accustomed to getting out-of-band emails for queue management.
A ticketing system lets people (and the company) optimize their workflow around it, customize their notification preferences, keep all documentation of an issue one one place, etc. By adding another communication system you are:
- potentially subverting the work flow
- encouraging documentation to evolve outside the ticketing system (in replies to your email)
You said nothing about the urgency of the issue, but I'll assume that's not really the question here. I've seen many cases where people started with a direct contact (e.g. chat, phone) and then logged a ticket as a place to document the work.