My understanding is that one of the benefits of modern synthetic lubricants is that they don't gum up. They may oxidise and lose lubricating properties but this will be a decade or so rather than months.
Have never had a problem with the accuracy of watches that have been idle for even for a few years (none are near expected service intervals though). All have been identical to where they were when I last checked (yes, I do keep a note and I am a saddo)
Thats a huge relief to know, thanks! Are modern synthetic lubricants quite common in watches and services these days, or is it something only making its way into common use very recently?