If we analyze that section carefully, the wording is quite specific:
(48) (A) The term "conviction" means, with respect to an alien, a formal judgment of guilt of the alien entered by a court or, if adjudication of guilt has been withheld, where(i) a judge or jury has found the alien guilty or the alien has entered a plea of guilty or nolo contendere or has admitted sufficient facts to warrant a finding of guilt, and(B) Any reference to a term of imprisonment or a sentence with respect to an offense is deemed to include the period of incarceration or confinement ordered by a court of law regardless of any suspension of the imposition or execution of that imprisonment or sentence in whole or in part.
(ii) the judge has ordered some form of punishment, penalty, or restraint on the alien's liberty to be imposed.
The mere entry of a plea does not cause an immigrant to fall afoul of the "conviction" statute. INA 101(a)48(A)(ii) requires the judge to enter some form of punishment.
In Superior Court, in DC (as is true in most Federal jurisdictions), one can get a DSA -- deferred sentencing agreement. In this case, the individual pleads guilty (satisfying (48)(A)(i)), but the judge enters no sentence. Instead the prosecutor and the accused enter into an agreement (say -- community service). The judge merely continues the case to a different "status hearing". After six months and completion of the agreement with the prosecutor, the judge accepts a motion to change the plea to not-guilty, and the prosecutor enters a nolle prose. In this case section (48)(A)(ii) has not been satisfied, so despite the plea, there is no conviction. These are common in most states -- SIS in VA and PBJ in MD, for example (although one must be careful in the approach, obviously, as mishandling this in state court could be a problem).
Generally, this means DSA's and DPA's (deferred sentencing agreements and deferred prosecution agreements), as well, are conviction avoidable.
Also, be careful to read the difference between arriving aliens (inadmissibility) and removable offenses.
Post conviction relief is not so cut and dry. In VA, it doesn't really matter what the snorkel the federal holdings are -- the Supreme Court of VA has said no dice to re-opening immigrant cases for lack of notice as to consequences. However, re-opening a case for substantive fault (i.e. procedural or factual defect) is always an option. Removal of the conviction = end of the immigration issue (although, again, you need to be careful as to which type of case this is removal or inadmissibility). I would also be delighted to argue that a case dropped in state court (regardless of the genesis of the convictions removal) ought to be sufficient to end immigration proceedings (it is hard as hell to get post conviction relief in most courts). Let the government prove it was done only for immigration purposes.
Finally, post conviction relief that does not remove the conviction, but changes the sentence, is also effective for changing the consequences in immigration court (I believe your handouts spoke about this). While not directly on point to what was originally brought forth here, it should still be noted that you might be able to get an agg-fel dropped to something...well...less than an agg-fel by get the underlying court to modify the original sentence to less than one year.
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