The recent SpaceX Pad Abort Test shows a parachute landing but I'm assuming a pad abort will also utilise the vertical landing capability for regular Dragon vertical landings right?
No, Crew Dragon will splash down in the ocean after an abort sequence. Crew Dragon only has 400 gallons of fuel for its SuperDraco thruster system. All of it is used to accelerate the capsule upwards and away from the Falcon 9 during an abort.
The abort burn was terminated once all propellant was consumed, and Dragon coasted to its highest point.
-SpaceX Pad Abort Test
Since Dragon cannot discard the motors after launch like a puller system, powered landings are a residual benefit. Crew Dragon has three landing modes: Water Splashdown, Parachute Assisted Landing, and fully Propulsive Landing. For the first NASA test flights and first crewed missions, Dragon will land with its parachutes in the ocean. Once the DragonFly test program progresses, SpaceX will attempt SuperDraco-assisted landings on solid ground. Once DragonFly has conclusively proven the success of Propulsive landings, actual crewed missions will be attempted with them.
No: Launch abort and propulsive landing both use the eight SuperDraco engines for which there is limited fuel. The beauty of the design is that the abort system isn't wasted mass when an abort isn't needed because it can be used for precision landing, but reusing the system means that when an abort is necessary there isn't enough fuel to perform the propulsive landing and it reverts back to a parachute landing in water.
This isn't as explicit a quote as I was looking for, but (from space.com):
And SpaceX engineers have designed the SuperDracos to serve as both launch abort engines, as well as descent engines. If a Dragon launched smoothly, the SuperDracos could then be used to make a land-based landing for eventual reuse.