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No. HOME stores unique data for each pokemon for each game. By creating a BDSP origin pokemon in SWSH or Legends: Arceus, HOME already expects that pokemon to have passed through HOME, and it expects to have already stored game specific data for BDSP. Since it didn't actually originate in BDSP, HOME looks for that data and finds nothing. It may resolve the issue if deposited into BDSP, but as a rule of thumb, HOME should "see" a pokemon for the first time being deposited from the correct game. Try to generate BDSP stuff in BDSP, LA stuff in LA, and SWSH stuff in SWSH.

Nintendo official magazine (UK) - April 2000 - pages 78-79 - has info about the Nintendo Official Magazine Tour 2000, you couldn't get a Mew at this tour, but if you won a gold badge, you could later trade this for a mew. Nintendo official magazine (UK) - July 2000 - pages 66-71 - Has some photos from the previous tour and an artical about one of the contributors going to Japan to collect a "mew machine" and a giveaway for 100 Mews. Nintendo official magazine (UK) - August 2000 - pages 70-71 - Has the info about the Nintendo Pokemon Tour with the Mew downloads. Nintendo official magazine (UK) - September 2000 - pages 74-75 - Has photos from the Bluewater Event Nintendo official magazine (UK) - October 2000 - pages 70-71 - Has photos from the Southampton Event Hope this helps you out. I went to the (Beumont) Leys event on the first tour, got knocked out pretty fast but got to play Stadium before the release. I got my Mew from the second tour at the Manchester stop, by luck as i was visiting family up that way. I still have it somewhere on a floppy disc (ha, remember those?), a local game store would make backups of your Pokemon games for £5!