Yes, you definitely can because those payment relate to your valid employment. You cannot stay in the USA though.
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Yes, that is a contractual issue, not an immigration one.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
I agree with the previous attorneys, except that currently under the H4 you cannot work. My question would be however is the payment for the non-compete be in the form of a payroll check, is it going to be a lump sum based on the contract. I recommend setting up an appointment with an employment law immigration attorney to discuss further