Can a non-immigrant on a A-2 visa file for immigrant status once here in the USA without having to return to the home country?

Most proxy marriages are not recognized by immigration law. You have to look into specific requirements to see if the procedures of your marriage complied with immigration law requirements. You did not provide enough facts for me to make a definitive determination. Once you are married under the Texas law however, your marriage will be recognized. Another potential problem is the misrepresentation of true intentions of your spouse's visit to the USA. That may land your spouse in an uncharted territory of a hardship waiver and potential legal fees associated with a very cumbersome process of going through it. You would be better served by taking your time and finding an immigration attorney in your area for a real and detailed consultation. May save you a lot of money later on. Do this, you will be glad you did.

Your "spouse" would be charged with committing immigration fraud if it is later determined that she entered the US with the intent to marry. You may want to discuss your options with an immigration attorney how to go about your situation.

I agree with my colleagues. The A1/2 visa requires the alien to have nonimmigrant intent when requesting entry at a port of entry. Furthermore, is a public site and there does not exist any confidentiality for postings --- ergo how many A1/2 visa holders going to enter from Ghana in the near future and marry someone in Texas.