No, how your original question was worded, I thought she did not qualify as a resident alien, that she had come to the US after you and the fact that you were asking about the form 8843 which is for people who are non-resident aliens, not resident aliens. Why are you trying to exempt your wife from the substantial presence test?
"If you are an alien individual (other than a foreign government-related individual), you must file Form 8843 to explain the basis of your claim that you can exclude days of presence in the United States for purposes of the substantial presence test because you: • Were an exempt individual, or • Were unable to leave the United States because of a medical condition or medical problem." Form 8843 If you are not tring to exclude days of presence for your wife, and she is a resident alien, you would not need to fill out form 8843. Also, unless she is a student or medically unable to work, she would not meet the criteria to be exempt. See page 3 and form of the instructions form 8843.
So, if your wife meets the substantial presence test, even though she is unemployed you would be able to file as married filing separately or married filing jointly. Without an ITIN or SSN, if you want to file as married filing separately, you would need to print and mail your return with an explanation IF she has also met the substantial presence test explaining that she does not have an ITIN or SSN.
However, since she is unemployed, your best option would be to file a joint return, include the W-7 with your return to apply for the ITIN. This would give you a standard deduction of $27,700 instead of $13,850 which would lower your taxable income which in turn would lower your tax liability.
