100% viable.

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Next races on the schedule: none at the moment

Sure can, running it on a felt ia16 rim brake bike. works perfectly

I think you can get away with not even using a blipbox now, as long as you have a way to do the initial sync of the rear derailleur and wireless blips.

edit: I missed the original part about running the shimano chain, etc. I don't know about all that.

I would match my chainrings, cassette, jockey wheels and chain to one brand. The AXS flattop chains have a different roller size than shimano. You can use HG+ tech with shimano if you get a 12s shimano chain and cassette. The jockey wheels are probably the least important to change, but I'd just do it for consistency.

Honestly, it'll all probably work without moving everything to the same brand, but I do find my HG+ bikes shift faster than the AXS bikes. And HG+ requires chain and cassette to match. It might be cheaper to get a 105 cassette + HED HG freehub than buy a campag cassette. The shimano cassettes and chain are cheaper than campag and sram.

Also, you don't need the blipbox if you have a friend/bike shop willing to setup the bike for you. You just need to find someone with an AXS shifter/blipbox. It could even be an AXS eagle shifter.