I don't think anyone has actually answered the question being asked here.
You can connect your Sky box to the DVD recorder and record to DVD or HDD (if available) as desired.
By means of a Proof of Concept - my kids recently managed to do this without meaning to - 6 hours of CBeebies anyone?
Whether you can feed the freeview signal back out from the TV to any other device, I don't know, but then as has been noted, you will have access to most/all those channels via the Sky box anyway.
I purchased a Sony DVD recorder at the end of last year and opted for a model with a freeview tuner as a possible pre-cursor to dumping SKY (in the event my aerial is not up to the job, can't pick up MUX1). Freeview tuners are becoming pretty much ubiquitous, a cheap and easy add-on to boost the feature list.
I would recommend you don't bother with the freeview option - assuming you can avoid it!