Almost a year later I stumbled upon this question to do the same and did a little research.
I found this interesting way in version 1.9.2 of the official mongo driver:
var query = Query.EQ("_id", 1);
var update = Update
.Set("field_timestamp_local", DateTime.Now)
.CurrentDate("field_timestamp_mongo");
collection.Update(query, update);
This code sets 2 fields to a timestamp, the first the local clients timestamp, and the second field to the server time.