Conviction of an aggravated felony is not at this time a ground of inadmissibility.  However, an offense that is an aggravated felony often makes the person inadmissible under some other ground.  For example, conviction of a drug trafficking aggravated felony is a basis for inadmissibility under the grounds relating to controlled substance conviction and the agency’s “reason to believe” that the person is a trafficker.  However, if the aggravated felony conviction does not make the person inadmissible under any other ground, or if a waiver is available, the person may apply for admission.  For example, a person convicted of a moral turpitude offense that is also an aggravated felony can attempt to waive the offense under INA § 212(h) under certain circumstances.  See § 2.45, infra.  A person who is deportable, but who is either admissible or inadmissible under a ground that can be waived, is eligible for adjustment of status[216] or immigration through U.S. consular processing abroad.

[216] Matter of Rainford, 20 I. & N. Dec. 598 (BIA 1992) (noncitizen can adjust although deportable under the firearms ground); Matter of Gabryelsky, 20 I. & N. Dec. 750 (BIA 1993) (noncitizen can adjust, although deportable, in conjunction with former INA § 212(c), 8 U.S.C. § 1182(c) waiver).

Other

RELIEF " CONSULAR PROCESSING " PROVISION UNLAWFUL PRESENCE WAIVERS
A practice advisory on provisional waivers of unlawful presence is available here: http://www.aila.org/content/default.aspx?docid=42954