It depends on what you call inexpensive.
If it were possible to do this, you would need a large amount of storage and network bandwidth to ingest all your tapes together – 25Mbits for each DV25 tape and more if you’re looking at DV50 or uncompressed standard definition.
You would also need to sync your recordings to keep your timecode together. Even then, you’ll have a mass of ingested media waiting for you to edit. It’s a balance between your time, your storage budget and your requirement to save time.
Avid do make a product called Capture Manager that can do this sort of ingesting but it is part of a broadcast infrastructure system requiring many hi-end systems working together and as such could hardly be described as inexpensive.
On the other hand, how many VTR’s do you have to hand that you can ingest from? Can you afford to tie-up your other systems?