Can internal linking create excessive
web server load?
Not unless your server is already struggling - Googlebot (unlike many poorly-conceived spiders and some recursive downloading agents) throttles requests and even allows webmasters to specify how often Googlebot should visit pages via Google Webmaster Tools (if your server is already struggling).
Can it be harmful?
Yes, because there are plenty of poorly-conceived spiders and recursive downloading agents out there which can bring your server to its knees if you've created interlinked quagmires (particularly so if these are resource-intensive dynamically-generated pages).
I am having a hard time seeing how your site's users benefit from this feature if there are hundreds of tags.
Wouldn't a site search feature be better-suited to users' needs?
Why is there a need to map up to five categories' union to a unique URI?