Here's a dictionary definition:
https://medical-dictionary.thefreedictionary.com/medical+condition wrote:
A disease, illness or injury; any physiologic, mental or psychological condition or disorder (e.g., orthopaedic; visual, speech or hearing impairments; cerebral palsy; epilepsy; muscular dystrophy; multiple sclerosis; cancer; coronary artery disease; diabetes; mental retardation; emotional or mental illness; specific learning disabilities; HIV disease; TB; drug addiction; alcoholism). A biological or psychological state which is within the range of normal human variation is not a medical condition.
Based on that, it sure seems to me that Aspergers is a medical condition.
As for whether you should put it on your medical ID, absolutely positively yes, especially if you have things like shutdowns or meltdowns. It could be extremely helpful to you if you were to ever have a bad episode of one of these in a public place.
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Level 1 Autism Spectrum Disorder