The converter box is just an
ATSC tuner.
I don't know of any VCRs or DVD-recorders with
ATSC tuners, but I'm sure some of the latter exist. However, that wouldn't "convert [your] television from analog to digital". Rather, having an
ATSC tuner just means that the DVD-recorder can receive digital broadcasts. Then, you can watch on your television whatever the DVD-recorder chooses to put out. Essentially, it depends on the DVD-recorder, but most likely you can watch on your television what the DVD-recorder is or would be recording.