In theory yes, saves in old formats should be readable by Doomsday version 2. However, I haven't tested it personally recently so it may be malfunctioning.
I recommend you make backup copies of the saves just in case, and then see if Doomsday 2 recognizes your saves. If successful, the saves will be copied and upgraded to the new format.
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I recommend you make backup copies of the saves just in case, and then see if Doomsday 2 recognizes your saves. If successful, the saves will be copied and upgraded to the new format.