In Netflix's "Atypical", does Elsa (Sam's Mother) have Asperger's Syndrome?

I disagree, I think she may be on the spectrum for sure

I’ve recently come to realize I was on the spectrum and that was after 23 years of living in ignorance. I had many friends- too many for that matter and I think it’s because I was never diagnosed it so I didn’t think of myself as weird or incapable so nothing held me back. People know me to be the most emphatic person they’ve ever met; autistic people are more than capable of feeling emphathy, we may even feel more than the average person; we just don’t know how to show it sometimes. Much like Elsa who you can tell cares a lot but the way she shows it isn’t “normal” like the average person would. Speaking as someone who’s on the spectrum but never diagnosed until older, Elsa shows many signs that she could be on the spectrum but never having been diagnosed so living a normal life (for the most part)

Also, her entire encounter when she first met the guy she was cheating with just screamed signs of being on the spectrum. She says a lot of random observations that could come off as “mean but true”, amongst other things.

Also, there’s a reason we consider it to be a spectrum. Some traits won’t be as strong, if any at all but that doesn’t mean she’s not on it. I find that there are many things that I struggle with but other things are just fine for me. And in some of my siblings, who I think may be on the spectrum too but slightly higher functioning than me, show some autistic traits that I have no problem while not having problems with the ones I struggle with.

Certainly it's not diagnosed. For any spectrum disease, such as autism or Aspergers, traits can be very mild or more severe.

In an article about the 10 Signs of Asperger's

There are several that she doesn't clearly fit neatly into:

1. Failure to Develop Friendships - while Elsa emerges herself in Sam's disease and leaves little time for herself, she genuinely seems to have a connection with other parents in her support group.

2. Selective mutism - Elsa isn't short on talking whether in public or among friends and family.

3. Inability to empathize - her life is trying to control the world around her sensitive son. She lives empathy.

4. Sticking to a routine. She does do this, but I think for the benefit of Sam who can't handle a lot of change. Her relationship with the bartender forces her to change her routines dramatically.

5. Poor motor skills. She is a professional hairdresser so she has control of motor skills.

Given she doesn't seem like a good fit according to the article I would say no. I think her character traits that you mention are more about establishing that she is stressed, on edge and has sacrificed her life for Sam.