It depends on the vendor and how they operate.
If a vendor has data collection for things related to downloads and programs and a cloud network then the answer would be yes. If a vendor does not then the answer would be no, because it wouldn't make a difference that way. Even if logs are anonymous, if a vendor has download links which were deemed potentially "suspicious" sent back to them then they can have teams go through them and pin-point the suspicious/malicious ones and add a detection to them quicker, but without such they may not have known of the URLs for hours later or days, etc.
Let's use a cloud network as an example. New cloud uploads for Win32 executables could be sent through an automated sandbox system once uploaded even if the original cloud scan was for file reputation, and then the vendor can add a detection based on the sandbox logs a few minutes afterwards if necessary. In a scenario like this, the more users means more cloud uploads which means more Win32 executable's which were previously unknown to the cloud are becoming known... Thus making the product more reliable with detection and reducing false positives and the user being protected better.
I mean there's many scenarios but it depends on each vendor (e.g. their privacy policy and rules) and how they operate their product (including the product's feature-set).
