MultiChain is an executable, rather than a script, so it depends on the level of access you have to the server. If it's only uploading PHP and static HTML/image/CSS/etc... files, then the answer is probably no. But if you're allowed to install and run your own software, then the answer is yes.
If it's not possible, you should probably run MultiChain somewhere else (e.g. on a cheap Digital Ocean instance) and then access MultiChain's API from your web server using an appropriate library, either general purpose JSON-RPC or you can try one of the third party libraries listed at the bottom of: https://www.multichain.com/developers/