Certainly taking it to your manager is a valid option, but I think you have some other options available before you try to make this your manager's problem. However, it is appropriate to keep your manager appraised of the situation. Privately in a 1-on-1, I'd mention that this coworker has been an impediment so far, and why, but I think you can also mention that you're taking some active steps yourself to keep things moving.
Here's some tricks I'd use.
1 Have a list
Sounds like there's more than one project that this coworker needs help with. Write up the list of everything you've heard of, and prioritize it as best you can. Vet the list both with the coworker and the manager - a group email should be fine.
2 - Clarify dependancies
In the list, clarify any you/coworker related dependencies at a high level For example:
- write code for test tool - you
- provide test environment - coworker
- install code on environment - you?
- provide feedback on test tool usefulness and needed fixes - coworker
- provide updates - you
Project = DONE
If you have more than 5 steps for an objective, it's probably too detailed. It just needs to be clear who is doing what, in what order and in words the boss as well as the coworker can understand. If it's a repeatable pattern, say so - for example, the list above is something that works on just about any project or feature in most software teams, replace "Test tool" with virtually any other type of code based development and you're list is probably accurate.
Share the list with the coworker and the manager. This makes the coworker accountable not just to you, but to management. If you've labeled a step wrong (perhaps you should know how to setup the test environment... perhaps he should test the installation of the feature...) - either he should step up and point it out, or the manager should.
3 - Silence = Agreement
Particularly in the case of dependandancies, don't write an open ended email. Write a time deadline driven message with a clear description of what will happen if a response is not received.
"Here's the list of tasks associated with our top priority objectives. Please take a look at the assignments and let me know if anything is missing or incorrect. I want to start the work by the end of the week, so please let me know by Wednesday. If I don't hear from you on Wednesday, I'll assume we're good to proceed and I'll start on my end of the work."
Thing to avoid:
"Here's my take on the list of tasks. I'm not really sure if you agree. Please let me know. I'll wait to hear from you before proceeding."
This would be a fine approach if you were talking to a customer or a person with authority over you or the project. For example, you can't write to a customer and say "I'm going to randomly do work for you and then send you a bill, if you don't tell me 'no' by tomorrow"... no matter how much you might like to. :) But where you are all tasked with the same goal, it's OK to say "I'm going to do what I understand to be my responsibility as quickly and efficiently as I can - so that you can do your end when you have time".
4 - Provide status
Often the original agreed upon list from step 2 is good enough. Work in a way that is kind to people who are busy, and don't make lots of words. A quick way is to take the original list and mark it up as follows:
- write code for test tool - you - STATUS = DONE
- provide test environment - coworker - STATUS = WAITING
- install code on environment - you? - STATUS = BLOCKED
- provide feedback on test tool usefulness and needed fixes - coworker - STATUS = BLOCKED
- provide updates - you - STATUS = BLOCKED
Project = Current status = 20%
If you've got a number of objectives, just move on to the next unblocked objective. Keep piling 'em up. Scheduling a meeting or promising to schedule a meeting does not count as reportable progress.
Again, CC the boss to keep him in the loop.
When you run out of tasks you can do yourself, it's time to go to the boss and say "Am I missing something? Was there something on this list that I can do or should do to move these projects along?" Don't talk about the other guy, make sure that you have covered everything you could reasonably do.
Is this mind numbing?
Yes. This is something that a strong team can work out without the boss. In a thrumming, high performing team this isn't needed. But you have case where accountability isn't being taken. You can take accountability for the overall status - but you can't take accountability for key tasks that you can't do on your own.
Often CCing the boss will make this real enough that your coworker will start to care. After all, you're not ratting him out, you're making the boss aware of a project that was important enough to pay you to do it. It's really easy to overlook people if they aren't pointing out that the lack of collaboration is making it hard to get anything done. But seeing one's own name next to a lot of unfinished, clearly worded tasks is hard to ignore.