Switch-mode power supply, and output voltage range - unregulated?
The 4.7-6.5V DC may well be within spec for charging a Blackberry (no idea) but on the Raspberry Pi the 5V side of the power supply has a SMBJ 5V transient voltage suppression (TVS) diode across the rail. That has a minimum breakdown voltage of 6.4V so at 6.5V it will be conducting to some degree and will possibly blow the 1A fuse which is a SMT part.

However if it doesn't blow the fuse the 5V rail also goes to the HDMI connector and the USB host connectors so it may cause problems with attached devices as well. I wouldn't recommend using that particular adapter and look for something that is regulated to within 5% of 5V as per the USB specifications, so 4.75V to 5.25V.

Also as Dave Tweed mentioned the Wikipedia article is incorrect (it mentions citation needed) and a switching power supply does not have to be regulated by definition. In this case however it may well be a regulated switch-mode supply, just one that is not regulated to a tight tolerance.

As per the updated question a typical linear regulator such as a 7805 has a drop-out voltage of around 2V, so that could end up being as low as 2.7V (if it works at all). Some low-dropout (LDO) regulators may be in the order of 200mV drop-out but as you may be starting below the specified voltage that wouldn't help getting things within spec the whole time.

The robust solution would be a buck–boost converter that can produce a constant voltage from a supply greater than or less than the output voltage. But in reality the cost / complexity would be greater than just purchasing a better supply.