是否在sick前加comma 會更恰當？

It'd better rewrite the sentence as:

Mary is sick at home, so I was not able to talk to her.

using a comma before sick is wrong.
sick is an adverb complement, telling you why Mary is at home.
The original sentence is a good one.
Ahshing actually changed the meaning and the main point of the original sentence. The main point is home (at home) sick is an additional information.

Both 001 and 002's answers are ok..
I also suggest you should re-write to this:
Mary is sick at home, so I am not able to talk with her. or
Mary was sick at home, so I was not able to talk with her.

The sentence's tense is depends on the time of the passage.

Another way to write:-Mary was unable to talk to me because she was sick at home.
Or use sequence of tense with live in the present time,not in the past:-Mary is sick at home,so I am not able to talk to her.
In writing without comma would be home sick=sad,think of Hong Kong when at England,usa,or foreign country.

2012-06-30 23:33:37 補充：
We live in the present,not in the past means I am not able;not I was not able.