My last day work will be December 31. I have four weeks of unpaid vacation. Can I start receiving my pension benefits on January 1 and continue to draw my vacation over the following four weeks?

Yes.  Assuming you have formally terminated your employment, you may choose a pension effective date the first of the month, following your actual last day of work, and you may continue to receive pay for vacation or sick leave from you last covered employer, as long as your Collective-Bargaining Agreement allows for this.