Orianna, Lady of Clockwork (Signature)

No. An equipment's effect text is inactive while Lady of Clockwork makes it a unit gear. Effect text is inactive unless its card is attached to another card.^136.2.b For example, a Cloth Armor unit gear's [Shield 2] ability is inactive, so it does not get +2 while defending.^721.2

The equipment detaches as it becomes a unit gear and remains at the same location as the card it was attached to.^718.6.a436.4 After it detaches, its effect text becomes inactive and its printed rules text becomes active again.^436.1.c The card it was attached to stops receiving the equipment's effect text and might bonus.^{436.1.d436.1.e}

You can activate and pay for the [Equip] ability, but the unit gear does not attach when the ability resolves. [Equip] is an activated ability.^818.1 You choose its unit target and pay its cost before resolution.^{818.1.b.1403.2405.1} Its effect then instructs the source gear to attach to that unit.^818.1.c.2 A unit cannot be attached, so the attach action does nothing.^{435.1.h435.1.h.1}

With either Shady Spectacles or Mirror Image, the resulting copy is a gear, not a unit.

While Lady of Clockwork's effect applies, the gear's current unit type satisfies the unit requirement for each effect's choice.^{141.1.a.3355.9.b} Lady of Clockwork changes the gear's actual type and might without changing its copyable traits.^479.1.c479.2 Copy effects use the gear's printed traits, the traits it had when created as a token, or traits supplied by an existing copy effect, so they do not include Lady of Clockwork's changes.^{479.1.b479.1.b.1}

The gear applies contested status to that battlefield, and the next cleanup stages combat if an opposing unit is there or a non-combat showdown otherwise. That combat or showdown opens after the chain is empty.

When Lady of Clockwork's ability resolves, the [Deploy] gear becomes a unit at its existing location. A unit that becomes present at a battlefield its controller does not control applies contested status there.^190.3.a The resulting cleanup stages a showdown.^323.7 If opposing units are present, it also stages combat.^323.8 A staged showdown or combat waits until no items remain on the chain before opening.^{323.11323.12331.2}

Lady of Clockwork's previous effect stops granting the old gear its unit type and might as soon as her controller chooses another gear during finalization, before the new ability resolves. If this leaves it as an unattached non-unit gear at a battlefield and it does not have [Deploy], the cleanup after finalization recalls it before players can respond.

Lady of Clockwork's gear choice is made during finalization.^403.2 Lady of Clockwork's stated duration therefore ends when the new gear is chosen, not when the ability resolves. Finalizing the ability makes a cleanup outstanding.^319.4 That cleanup must finish before play proceeds.^334.2.a The new ability cannot resolve during it.³²⁰ Priority is not passed or awarded during it.^320.1 During that cleanup, an unattached non-unit gear at a battlefield is recalled unless it has [Deploy].^459.1

The equipment stays attached when Lady of Clockwork's unit gear stops being a unit. The equipment is the attached card, while the unit gear is the top-most card.⁷¹⁷ Only the attached card must remain a non-unit.^718.6 It remains attached until something detaches it.^718.1 If the gear is recalled after losing its unit type, the attached equipment changes locations with it.^719.3.a