I see no issues with that plan and actually plan on using my keezer for a lagering compartment as well. However, I was planning on making this a two-part process. For the first 2-3 weeks when brewing a lager, you'll want the temps up in the 50's. Although my keezer can keep temps that high, I like my beers served right around 40F. Because of that, I'm thinking about putting together a small "Son of Fermentation chiller" for the initial time in the primary. Once I'm ready to lager, I'll just take my carboy and drop it into my keezer at 40F. Let it sit it out in there for the rest of the lagering period before kegging.
"Brewers enjoy working to make beer as much as drinking beer instead of working."