Maybe. I would trace them the other way to understand what loads are already on that circuit. You would also need to know what the draw of the pump motor is. Since you have traceability back, do you have the ability to pull a new wire? Do you have a spare fuse position in your power distribution? I would probably just run a new line if I could; then no worry about overloading a circuit.
Is that the only water line to the sink as well in the pic? If yes, you have no pressure plumbing in the pup? That means you will need to add some pex between the pump and the (new) faucet to handle the pressure flow side of the pump. If you also have external water, you will want to research how to properly plumb into that system so that you can use either source.
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2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2018 Nissan Titan Midnight Ed.
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