Yes, but it depends on the product and the Surface you buy.
If you buy Surface RT, or Surface 2, then you'll be able to visit websites that use Flash for streaming and it should work fine. If the website uses anything other than Flash (even Microsoft's own Silverlight) then it will NOT work, and it is absolutely not possible to install any plugins on Surface RT or Surface 2. This is the same as an iPad or Android tablet. NO PLUGINS! The only exception to this will be if the streaming service has written an app for the Windows store that plays their streams.
If you buy the Surface Pro 2 however, then you have the option of installing plugins, so whatever weird and wonderful plugin a streaming site might happen to use - then you can do it no problem. Be warned however - junk up your tablet with too much software and plugins and the nice smooth experience that many tablets deliver 'out of the box' might start to degrade! Nevertheless, compared to other tablets, those that run 'full Windows' like the Surface Pro 2 are clearly much more flexible, and if that's something you need then it could justify the extra money.