You should be able to. It depends on how their blocking foreign servers.
If they have blocked access to foreign SMTP servers by simply stopping stopping port 25 at their firewall, it is possible to set up an external SMTP on a non-standard port. A good number of mail clients can be configured to communicate SMTP on a non-standard port.
If they are doing some kind of packet inspection, there's not much you can do.
ISPs do this for a good reason. It stops some spammer from opening a temporary account, send out 1000000 emails advertising some bad site, closing the account without paying, then leaving the ire of the internet to fall on the ISP.
Why do you want to not use your ISP's server?
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Perfection in engineering does not happen when there is nothing more to add.
Rather it happens when there is nothing more to take away.