According to the rules of the Terminator franchise nothing can go through the time portal except living things. Therefore, Cromartie's all metal head could not have been sucked through the time portal with John, Sarah, and Cameron when they jumped from 1999 to 2007.
When Cameron is battling with the other terminator they both go out the window, hitting the wall of the adjacent building and falling to the ground. Look carefully as they hit the wall and you can see it move.
While it is certainly possible for Cromartie's body to survive the bank blast, It seems unlikely that Cromartie's unique skeletal remains would go unnoticed as something special while clearing up the bank's remains. In addition, his unique skeleton would not be tossed into a junk pile and also would most likely not go unnoticed for 8 years.
Sarah, John, and Cameron arrived in 2007 from 1999 with nothing, no clothing, no cell phones, no money, nothing. Yet within three days they have a house, cell phones, new clothing, and some money. While it is possible they stole some items, it would be hard to rent a house and get cell phones with no IDs.
Enrique refers to a boxer called "El Finito" and Sarah instantly translates that for "The Finisher". While Ricardo "Finito" López is a real, legendary Mexican boxer, Sarah's translation of his nickname makes little sense. Out of context, the word could mean "slim" if translated from Spanish and "finished" if translated from Italian, which is its real origin, but not "The Finisher".
There's a recording of El Finito talking at the end of the episode. In it, he says "expensivo". Expensivo is not a real word, and no native Spanish speaker would ever say that.
When tested on his new identity by Cameron, John says he comes from Lawrence, Kansas, and Cameron says his father was a police officer who was killed in the line of duty. Later (while registering for school) we see his fake birth certificate which says he was born in Los Angeles to an unknown father.