No you cannot. There’s no access to non-thread safe components or the DOM and you have to pass specific data in and out of a thread through serialized objects. So you have to work really hard to cause problems in your code. jQuery is a JavaScript DOM library.
But you can use a native XMLHttpRequest
in your worker however.
And, importing external scripts does not go via the page with a script
tag : use importScripts() for that in your worker file.