Yeah, some VPN providers block ports that accesses SMTP to prevent spammers from abusing the service. The only way to use email and VPN at the same time is use split tunnelling. Some VPN client software offers a network level split tunnel setting that enable SMTP access outside of the VPN while you're surfing anonymously. To check that you are still anonymous and the VPN is still protecting your identity while sending email, you should first check anonymity with proxy test.
Some VPN proxies only provide partial anonymity. A high anonymity proxy changes your IP address without revealing to the website you are using a proxy, while others will change IP address, but they also inform the website you using a proxy (partial anonymity).