What most likely happens is the software "sends" the emails to the mail queue of your server (in my case it is Exim). And then they will sit in the mail queue until your server is able to send them. So if there is a bottle neck in the actual sending (connecting to the other mail servers, etc.) then even if mailwizz is sending faster than that, it won't be a problem because the messages will go to the exim mail queue and the server will handle them when it is able to.
In my server I can "send" 250,000 messages in one or two hours from mailwizz using redis. From there it is transferred from redis queue to my exim mail queue at roughly the same speed (nearly instant). Then the exim mail queue builds up a backlog and it takes a few hours to actually deliver the messages to the remote mail servers and empty out the exim mail queue.
So you could probably actually handle sending thousands of messages per minute through mailwizz, though you have to remember they aren't actually being delivered to the remote mail servers at the same speed.