Of course you can.
Entering the United States without being inspected and admitted, i.e., illegal entry, is a misdemeanor or can be a felony, depending on the circumstances. 8 U.S.C. § 1325. But many undocumented immigrants do not enter the United States illegally. They enter legally but overstay, work without authorization, drop out of school or violate the conditions of their visas in some other way. Current estimates are that approximately 45% of undocumented immigrants did not enter illegally. See Pew Hispanic Center, Modes of Entry for the Unauthorized Migrant Population [May 22, 2006].
Undocumented presence in the United States is only criminally punishable if it occurs after an individual was previously formally removed from the United States and then returned without permission. 8 U.S.C. § 1326 (any individual previously “deported or removed” who “enters, attempts to enter, or is at any time found in” the United States without authorization may be punished by imprisonment up to two years). Mere undocumented presence in the United States alone, however, in the absence of a previous removal order and unauthorized reentry, is not a crime under federal law
8 U.S. Code § 1325 - Improper entry by alien
(a)Improper time or place; avoidance of examination or inspection; misrepresentation and concealment of facts
Any alien who (1) enters or attempts to enter the United States at any time or place other than as designated by immigration officers, or (2) eludes examination or inspection by immigration officers, or (3) attempts to enter or obtains entry to the United States by a willfully false or misleading representation or the willful concealment of a material fact, shall, for the first commission of any such offense, be fined under title 18 or imprisoned not more than 6 months, or both, and, for a subsequent commission of any such offense, be fined under title 18, or imprisoned not more than 2 years, or both.
I'm not guessing here. I do this for a living. I've made the arrest. This would be like me telling you about O&G.
I'm not doing this all day. Believe what you like with black letter law staring you in the face all you like.