Not really. And you're better served obtaining an FBI rapsheet. It costs $18, requires your fingerprints and takes about 10 weeks to receive a response. The response will be most closely aligned to what USCIS / DHS sees as your history.
They may be able to get the record just as you would but they will not be able to avoid any fees and it is generally more efficient if the client obtains it because most attorneys bill for their time. Can they "make a couple calls or something?" No.
I agree the best option is the FBI background check.
Legal disclaimer: The statement above is general in nature, 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.
There are two ways to get a criminal record: (1) FBI Prints, the cost is only $18 with the FBI and takes 2 months; (2) go to the local court and request a print out with a name search, the disadvantage is that you will only get a record of an issue you had with that court and none other, but if you know the court where your criminal issue was filed, then this would be the cheapest and fastest way. If your attorney has a great relationship with the Clerk, then maybe s/he may be able to get that information over the phone, however, for any immigration process, you WILL need a certified copy of the disposition.
The answers provided should not be considered legal advice. They are for general information only. It is always recommended you consult with an attorney prior to taking any action.
You need to hire a criminal defense attorney and/or an immigration attorney to get all your criminal records and review them as to their impact with ICE. Don't be foolish about saving money, spend it and get good sound advice.
I am trying to give you a general answer to your question. We do not have an attorney-client relationship by this response on the avvo website. I have not been retained to represent you. I am licensed to practice law in Kentucky and in federal court in this state and the Southern District of Indiana. You need to seek legal advice from an attorney licensed to practice in your area..