A tunnel like this should be insanely expensive and should take a very long time to dig. It wouldn't be easy either. If you make it a shallow tunnel, you need to potentially deal with burrowing creatures getting into it, and you need to haul in a lot of stone to build roads (otherwise underground trees may block the tunnel). If you make it a little deeper, you need to deal with digging around aquifers and rivers. If you dig even deeper, you might need to deal with caverns or magma pipes. If you dig deeper still, you'll definitely have to deal with caverns, and all the creatures they contain. No matter what, it won't be easy or cheap.
Let's assume we pay each dwarf working on the tunnel a salary of 500 dwarfbucks per month (this includes hazard pay). Let's assume the digging team will consist of 3 miners, 3 masons, 30 haulers (carrying food and booze from the home settlement, and moving stone as well as beds, chairs and tables for everyone...), 1 architect, 3 doctors, one squad of 10 axedwarves, and one squad of 10 marksdwarves. There are 60 dwarves in this digging team, so you'll need to pay 30,000 dwarfbucks per month of digging. Since the caravan comes once per year, you should pay in installments one year at a time, so you'll need to donate 360,000 dwarfbucks before they get started on construction.
Construction time should be, on average, about two months for every normal embark tile they need to pass through, six months for every embark tile of river they need to cross, and a year for every embark tile of ocean or lake they need to dig under. Your distance to the nearest inhabitated dwarven settlement would determine exactly how much time and money would be necessary to complete the project.
Once the tunnel is built, you'd want to have guards patrolling the tunnel routinely to ensure that you can kill any weak underground creatures, to warn you of any possible invasion through the tunnel, and to identify any problems that will require maintenance. Assuming you have two squads like I suggested above, and assuming they bring 20 haulers and 3 doctors, you'd need to donate about 250,000 dwarfbucks per year to keep the tunnel open. If they run out of donations to keep the tunnel open, they can seal it up until you're willing to donate more money for it.