Possible? Possibly yes, but it's going to take some work.
For starters, you will need to write a custom WCF Transport Channel that handles the specifics of your TCP/IP based protocols (i.e. you'll need to write all the socket handling code and hook that into the WCF channel model). This is because the TCP channel in WCF isn't for this kind of work, but uses a relatively proprietary and undocumented wire protocol.
I'm not familiar enough with FIX to say how complex it would be, but there are some gotchas when writing WCF channels and documentation in that area isn't great.
The second part you'll need to deal with is message encoding. To WCF, all messages are XML. That is, once a message is passed on to the WCF stack, it has to look like an XML infoset at runtime. FIX doesn't use XML (afaik), so you'll need to adapt it a bit.
There are two ways you can go around it:
The easy way: Assume the server/client will use a specific interface and format for the data, and have your channel do all the hard work of translating the FIX messages to/from that format. The simplest example of this would be to have your WCF code use a simple service contract with one method taking a string and then just encapsulating the FIX message string into the XML format that satisfies the data contract serializer for that contract. The user code would still need to deal with decoding the FIX format later, though.
Do all the hard work in a custom WCF MessageEncoder. It's a bit more complex, but potentially cleaner and more reusable (and you could do more complex things like better streaming and so on).
The big question though is whether this is worth it. What is your reasoning for wanting to use WCF for this? Leveraging the programming model? I think that's an important consideration, but also keep in mind that the abstractions that WCF provides come at a price. In particular, some aspects of WCF can be problematic if you have very real-time requirements, which I understand is common in the kind of financial environment you're looking at.
If that's the case, it may very well be that you'd be better served by skipping WCF and sticking a little closer to the metal. You'll need to do the socket work anyway, so that's something to consider there.
Hope this helps :)