While Kathy was pregnant with Eli, Elliot was involved in a case where a young boy's paternity turned out to be the product of his mom's affair after it was long believed that her husband was the father. The father was devastated after he found out the truth; he asked Elliot "What if?" one of his children turned out not to be his? Elliot then questioned if he was the biological father of Kathy's unborn baby. Elliot tried to question Kathy about the time while they were separated- if she saw anyone? Kathy admitted that she did date (nobody Elliot knew). He then asked if she slept with him but Kathy wanted to know why he's doing this? He wanted to know until Kathy questioned if he was really asking her if the child was his? But Elliot was called away before answering her. The next day, it wasn't until after the baby was born and Elliot was holding him that Kathy told him that he was the father. Elliot knew.
He must have thought back in retrospective while rushing to Kathy's side after her car accident. It was true that Elliot and Kathy were still separated at the time of conception. Although they were also considering to get back together. Elliot turned to Kathy after a case rattled him; he saw their children safe and sleeping soundly. Kathy invited Elliot to stay. They made love that night on March 23 (according to those DUN DUN banner dates). On May 16, Kathy informed Elliot that she was pregnant- about 8 weeks/2 months and he did not questioned at all if he was the father. Elliot was stunned but he moved back home and started to look forward to the birth. He worked for SVU where paternity issues came up often but it never occurred to him until that particular case. Since that brief doubt, Elliot never questioned it again- Eli was indeed his son.
Former Executive Producer Neal Baer confirmed it on this twitter when he was bombarded by that question.
In my opinion: I honestly believe that Kathy would never lie to Elliot- why would she? They've been together for a long time and after being in a car accident and was close to losing her life, there's no reason to lie about the paternity. Kathy looked stunned herself when she told Elliot that she was pregnant. Kathy seemed the type that if she's going to have a baby with a man, then she would want that man to be involved in the child's life. In addition: Elliot sure picked a bad time to questioned the paternity issue. It would've been better at the moment Kathy told him that she was pregnant/before he moved back home. Not when she's about to pop!