Does using Activity Monitor have an effect on server performance? Our SQL Server VLDB is being monitored by Activity Monitor on a networked machine.
95% of all traced statements can be attributed to this tool, but is it known to have a negative effect on server/network?
YES. Beware of the "observer effect."

This article is about you using trace and extended events directly, but Activity Monitor uses similar technology under the covers - it doesn't have any magical, no-cost ways of collecting performance information.

There are several monitoring tools out there that do a better job at this than Activity Monitor, some more so than others. There are also free scripts like sp_whoisactive and sp_BlitzFirst that are more honest with you about what's really going on on your servers (see this article). I strongly suggest you try some of those out and don't open Activity Monitor or Profiler at all.