It would surprise me greatly, indeed, if it proved to be the over-consumption of CPU time that is causing “everything else to become painstakingly slow” such that “web pages time out,” etc. It is almost axiomatic to me that such disruption actually comes from the over-consumption of virtual memory (leading to thrashing), or very inefficient use of the file system, or sometimes, simply having too many processes or threads fighting for available milliseconds. If this be so, then changing the dispatching-priority of a thread won’t help much at all, if at all.
Now, thread priorities do make a noticeable difference in some GUI systems, most notably Microsoft Windows, which still to this day is very sensitive to main-threads which do not timely respond to GUI messages. But this manifests itself as “visual jitterbugs,” such as mouse cursors that don’t move smoothly, even as other activities which do not directly involve the GUI continue apace.