Would completing this checklist be sufficient to claim the medical device is IEC60601 compliant? as opposed to going through an external testing body?
What market and regulatory system are you aiming at, and what is the reason for compliance?
Some FDA classification codes define IEC 60601-1 as a relevant Recognized Consensus Standard. A 510(k) premarket notification for a product in one of those classes will be most easily accepted if it includes evidence of conformance. Third party testing is an easy path to that evidence, but depending on the class I believe in-house testing is viable as well. In-house testing will require much more documentation, though, since you'll have to establish your calibrations and other measurement equipment validations, your technique conformance to measurement method standards, your personnel competence, etc.
Another common reason for compliance in the US market is that a number of inspectional jurisdictions...primarily large cities...won't approve the installation of electrical equipment unless it's Listed, and the Listing must be obtained via determination of standard conformance by a major test lab.
We also have heard of hospitals that have been told by their insurors in regard to potential major imaging system purchases that only Listed systems would be eligible for inclusion in their insurance coverage. I've heard of another instance where end users felt that they had to buy Listed equipment in regard to their JCAHO compliance stance, though I don't fully understand that one.
If your goal is to be able to support a marketing claim, at least in the US market, I'd think that in-house testing, competently carried out with appropriate documentation of course, would be fully sufficient.