You don't really give enough information to answer the question categorically. The short answer should be "No.".
Is your internal DNS just a caching nameserver? If so, it will read the MX record from upstream and all will be OK.
If your doing anything tricky, like DNS masquerading or similar, then all bets are off.
Have a look at
http://www.dnsreport.com to chexk it out. Plug in your domain name and it will tell you if all is well or not.