That's the way I did mine last year, and I think most do it that way but at low storage temps (kept mine in a spare fridge at around low 40's). Aged it right into September, brewed in March. As long as you keep it cold you should be ok. It doesn't have to go down to close to freezing, imo. Get it as cold as you can. You are still going to probably not get the clean profile of a Lager though, but as far as there being any trouble with aging in the secondary I don't see anything.
Event Horizon ~ A tribute to the miracle of fermentation.
Brew what you like. Do this, and you will find your inner brewer.