different db stats in MongoDB replica set
Logically answer is YES.

When I tested on our multi terabyte DB's, I got differences between replica set members, however this was measuring mistake, error on the procedure. f.ex. db.stats() is not good command, because RS node can have db.system.profile -collection, what is NOT replicated to other nodes.

How to do it right (do these on all replica set nodes):


Stop all write traffic to MongoDB, you can do that by closing all clients OR giving (at Primary) command db.fsyncLock()
select right DB (use xyz) and give command db.setSlaveOk(true)
Don't use db.collection.find().count() or db.collection.count(), use command db.collection.find({_id:{ $gt: MinKey, $lt:MaxKey} }, {_id:1}).itcount() to count how many documents there is
After you have done these itcount() commands on multiple collections and you are happy (or not) to result.. Don't forget to give (at primary) command db.fsyncUnlock()


we had maintenance break and I did this counting procedure during it and got (this time) right result. Every RS node had same count of documents. ;-)