The excessive pulsing will blow out the membrane in the gauge, so yes, letting it run that way will eventually damage it.
The gauges you have are 1/8 NPT, what you need is a 1/8 BSPT male to 1/8 NPT female adapter. McMaster-Carr (
http://www.mcmaster.com) is about the best place. I looked everywhere for some fittings just a few weeks ago. They have a very easy to navigate page. You want 'Pipe and Pipe Fittings' under the Pipe, Tubing, Hose and Fittings section. Then drill down, 'brass pipe fittings and pipe', 'adapter', 'female x male adapter', 'BSPT male x NPT female' then 1/8 inch. $3.91 each. That adapter would screw onto the gauge end of copper, then onto your NPT gauge.
I am using an oil filled gauge to help dampen the vibration, but with a large enough capillary you would not need the oil filled.