Hi,
I've never heard of TrixBox but did some searching....is it this one
http://www.trixbox.org ? Looks like a Linux based system running Asterix PBX software. Not sure if it supports SIP or MGCP or H.323.
If that's it and it supports SIP, then the answer is no. The IP Office doesn't currently support SIP. It is planned for v4.0 which will be nearly next year sometime. This will support SIP trunks so you should be able to link the two systems then. In v4.1 (or possibly later) IP Office software it will support SIP end points.
Depending on the abilities of the TrixBox, you may still be able to do it but it would be trial and error. The IP Office supports H.323 so you could try creating IP Lines in it and the same (if possible) in the TrixBox. I don't know if this would work but you won't get a straight answer out of Avaya. I've tried, and know others who have tried, linking the IP Office to other systems in this way and had no luck. SIP is really what you need to be able to do this.
Also depending on what the TrixBox supports and which country you're in, you could use BRI circuits to link the two systems using QSIG. This would give you basic functionality ie calls, CLI, name display etc
Hope this helps.