Can you print both sides without the impression showing through?
We regularly print double-sided cards and invitations, etc on our letterpresses.
The impression does not punch through the opposite side, since we use an appropriate amount of impression for the thickness of the stock, and a hard packing behind the piece on the tympan of the press.
Depending on the character of the stock, there will be a certain amount of change of texture, as the fibers in the high-touch surface are flattened against the tympan by the impression. There will also, obviously, be flattening of any prior impression opposite the side being printed. In practice, this is rarely noticeable, but the designer of double-sided work should be aware of it.
On our high-touch double-thick stocks (220# / 600gsm) which are roughly 40-50 point (.040-050") (Arturo, Savoy, German Etching, Copperplate Etching, Crane Lettra, Legion Bamboo), we are able to take full advantage of the thick, compressible fiber for deep impressions, including "blind" (inkless) impression. But even on the single weight stock, such as the Strathmore 130# Writing Cover, or Lettra 110#, we get very good results from inked impressions.
While we can arrange for flat (offset or digital) printing on the 'B'-side of the piece, we do this only for technical reasons (full-color, heavy solid coverage, halftones, etc) rather than for economic reasons. Due to the costs involved in set-up, outsourcing offset printing will add more to the cost of the project than having the B-side printed by letterpress.