Yes, it is possible. The device is compatible and can connect to the local 3G network (Turkcell) with minimal hassle. In addition, even though I had to purchase a two-year T-mobile subscription with my phone, the device is unlocked!
Disclaimer: I purchased this phone directly from Google in May 2010. Google is no longer doing this.
As soon as I landed in Istanbul, I went to the Turkcell kiosk, registered my IMEI number, purchased a prepaid card, and activated it. You MUST register your phone with the government agency or it may be banned permanently.
The next step is to subscribe to the 3G internet service. There are two types of 3G services:
1. Faturali (invoiced) 3G Internet
Subscription for this plan is automatically renewed every month. And there is an overuse charge which is currently 0,050 TL/MB.
2. Faturasiz (non-invoiced) 3G Internet
This is an on-demand plan which is limited by time and/or usage. It does not renew automatically; you need to repurchase it at the end of your subscription period or if you hit your usage limit before your plan expires.
After getting a prepaid card, activating a 3G plan is as simple as sending an SMS message to the appropriate number defined on the links above. [In my case, I was not properly briefed by the sales people at the airport kiok so I ended up purchasing the first plan.]
The last step is to do a little bit of setup. Go to Settings > Mobile Networks > Access Point Names, click on Turkcell, and set the APN to "internet" - without quotes.
You should be able to connect to the Edge network. If not, reboot your phone. Some time later (for me it took over a day) you should receive an SMS confirmation message for your 3G subscription request and the 3G icon should replace the Edge icon. (There is an unnecessary opt-in process after you purchase a 3G package. It should happen automatically. If not, simply call the support center.)