I've done some testing with Quicksilver Storm and Perpetualis, and when under the effects of the Overload Auto/SMG seasonal perk, both Untangler and Unraveling did not work at all, though could still gain unraveling rounds for the associated fragment from Strand. With the Thread of Propagation fragment equipped, Alliend Unraveling would not work, though Untangler still did. I am unsure of the latter interaction is intentional, but I would hope it isn't.
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Update: I have discovered the Allied Unraveling artifact perk does not work when all available fragment slots for Strand on Hunter are filled. Unsure if this happens on other classes as well.