yes with thisATI Radeon 5770
Apple Mini DisplayPort adapters: Frequently asked questions (FAQ)Guide to Apple graphic display adapters needed
The ATI 5770 has two mini displayports and a DVI output, so everything gets its own port.
I've got two 27" monitors and a 37" HDTV (all 1920 x 1080) on my 5770.
You'll need ACTIVE adapters on the MDPs for whatever input your displays are, like the Accell B087B-006B UltraAV Mini DisplayPort to DVI-D Single-Link Active Adapters I got on Amazon. They're about a third the price of the Apple part, tidier to install, and work great. I run the HDTV off the DVI port with a DVI-HDMI cable
7300 is over 7 yrs old has 256MB and lacks some of the newer feature specifications.
Some more info about using 3 displays and when you do and do not need active or dual-link (and your 23" ACD doesn't)Atlona (Dual Link) DVI to Mini DisplayPort Converter for Apple 27-inch LED and 27-inch iMac
Mac Pro (Early 2009), Mac Pro (Mid 2010), Mac Pro (Mid 2012): Issues with three displays and multiple DVI, HDMI connections
It's not the USB data that is needed to run three displays. It's the extra POWER.
In the Apple article, they say the only solution they endorse is their US$100 Dual-Link adapters.
Check the table at the end of the article.
Mac Pro (Early 2009), Mac Pro (Mid 2010): Supported display configurations
Readers here have found that if you have two Brand-X Powered adapters, aka active adapters, it also works fine.
These do not always require another USB. If designed recently, they can pick up a power pin in the Mini DisplayPort interface.
AMD (makers of the 5770 and 5870) lists the qualified POWERED adapters that meet their most stringent requirements. Look down the page and you will find several qualified Active Mini DisplyPort to various others, such as HDMI. These adapters are available from other outlets, such as Amazon, sometimes for far less than the Apple adapters.
The other desktop monitor will plug directly into the DVI port on the card and the 40 inch tv will still connect via HDMI over the second Mini Display port.
That will work only if you use an active Mini DisplayPort to HDMI adapter.
The only (someone) have found to work (2009)
You can connect a DVI to HDMI adapter or cable to an active Mini DisplayPort to DVI adapter but that won't give you any audio over HDMI. You could connect the DVI displays to the Mini DisplayPorts with active adapters and use a DVI to HDMI cable or adapter from the DVI port to the TV.
If you want audio via HDMI, you can use audio from the Mac Pro's optical output with this DVI to HDMI converter:http://www.apogeeinc.net/products/item.aspx?item=2745
Active MDP to HDMI audio and video converter:
Discussion: Using three ports.