Yes, it probably will speed things up. As things are, various elements on your page are probably kept waiting while the video loads. Professional platforms like Vimeo (I think) and Wistia (definitely) will load the video asynchronously, so the hit to your page load time is minimized.
This way all your server has to load are the on-page elements, which no longer include the video, but do include an iframe link to Wistia/Vimeo/etc. You may notice a particularly impressive speed increase for mobile users.
As with any such changes, you should test this sort of thing on one page before rolling it out across all of your sites. Use Pagespeed tools to assess the impact, as what has a huge impact on one site may not on another.