With any Bluetooth-enabled phone, technically, you should be able to connect your computer to the Internet across this phone as a standard modem. However, you may want to ask Verizon if they have a "Mobile Office Kit" for this particular device. If they do, order this, and install it on your phone and your computer. This should allow you access to the Internet. If they do not, there are many other ways to go about connecting your computer to the Internet through this phone. Some ways are legal, and some ways are not; you need to check with Verizon's legal team to ask if you can unlock your phone's Bluetooth profile for a modem if it has not been done already. You can also try connecting to the phone using custom hardware; generate a dialtone, connect a modem to the audio input and output ports on the phone, and dial your phone using a modem. Finally, if you've paid for this phone already (not rented or leased), then you can reload the Treo with an alternate operating system, such as Linux or BSD, and install a routing daemon, a Bluetooth network profile, and software to connect to your service provider. (The last method is probably the most difficult, and I do not encourage you to try it, especially with an expensive PDA phone!)
If you have the ability to connect to a virtual Bluetooth network on your PDA, you can attempt to setup a gateway daemon on your PDA, or attempt to load and use a SOCKS server on your PDA, and sending all of your requests on your computer through your PDA.
I hope this is helpful!
PS: If you're talking to the Verizon Wireless team, be persistent, and if they decide not to service you, remember that you always have freedom of choice.