Plumbing – Anyone know much about drill pumps

Short answer. In my experience as an HVAC technician:

There is no completely silent condensate pump on the market that Me or my Suppliers are aware of. If there was, everyone would be buying them.

There are however certain pumps on the market that are designed to take into consideration sound level. The quietest pump i have ever come across is the DiversiTech ClearVue Condensate Pump. They have great build quality along with all DiversiTech products, and also has a built in alarm and over flow sensor that can be wired into your HVAC system to stop operation of the air conditioner if there ever is a blockage in the discharge line, or if the pump should fail for whatever reason.

There are three reasons why you need not worry:

UL/CE rating

I think you will find it is UL or CE rated I know with UL the items are tested and abused like any home owner would, not as sure about CE but some equipment I helped build to send over the pond had 3rd party inspectors checking every part to make sure it could be CE compliant. The pump should have a GFCI plug this would limit any potential shock if the cord were to fail. I would think the plastic pump impeller would fail before the cord even with 5/6 years outside.

Connection

Should the device be faulty, you still need not worry too much. You will deposit it in your sitting pool of rain water, while it's not powered. You'll walk to connect the power cable (hopefully your outdoor power is a GFCI one). While connecting the power, you'll not be close to any water.

Weight

The vinyl tarp can already handle a column of water 2ft (maybe) high. If you calculate the distributed weight of the pump on the (usually large) base, you'll find that the psi on the tarp will be in the same ballpark as the column of water.

Just as importantly, you do want the weight of the pump to push a little on the tarp. That incline will drive all your rain water towards the pump so all the water reach it.