|Bad idea unless all you want is the convenience. These kind of services are major targets for hackers, and if you are using a free one, then you have to question how much of their resources are being put towards robust security. |
Recently one of the biggest name VPNs was found to have had one of their servers hacked by a careless network manager leaving remote access software active on the server that should have been deleted. Everyone who had connected to that server for the period of time that the exploit went unnoticed had their personal information (including all kinds of sensitive stuff that should have been encypted) exposed and more than likely recorded by the hackers.
If VPNs can get hacked, then free to use password managers can, and an NSA DEFINITELY doesn't want their passwords exposed to black-hats.