Will an unlocked Motorola Razr function as well as a locked Razr
purchased from the wireless carrier?

T-Mobile sells the Motorola Razr in silver but not black, so I am
thinking about buying an unlocked black Motorola Razr from a third party. 
My understanding was that an unlocked phone will work just as well as
a locked phone, but a T-Mobile representative told me that signal
quality would be slightly degraded since an unlocked phone has not
been optimized for the T-Mobile network.  Is this true?

That is somewhat true.

The "locking" is basically just setting up the phone to handle the
data capabilities of the phone, such as SMS, internet, etc.

Calling wise, your "signal strength" will not be degraded whatsoever.

Many phones can have the above things manually set by the user.  The
razr, being a brand new phone, should have this capability.  T-mobile
technical support should be able to give you these settings over the
phone.  I'd call and ask them first, before buying said phone though.

A quick google search yieled Motorola Mobile Phone Tools Version 3.0:
http://www.cellphonemall.net/wireless/store/accessorydetail.asp?id=41525

A product that contains "Preconfigured data network settings for most
major wireless operators gives you easy access to the Internet from
your mobile phone almost anywhere Send and receive Short Message
Service (SMS) over the wireless network and also email messages from
your PC"