Yes, Jack could have possibly gotten on that panel— not door— as well and ultimately survived.
However, there are some variables that James Cameron tested, and I will break them down for you if you don't have an hour to spare at the moment and want to know right away.
First, Jack and Rose would have to be in a state of mind to try the multiple positions on the raft needed for them both to get on the paneling without it capsizing. No matter how prepared they were, they would still to go into cold shock at some level, then hypothermia.
Second, they would need to be on the raft in a very specific position and within a certain time frame for Jack to survive. One position where they both were on, they both were partially submerged; enough to still doom Jack. Rose had enough insulation going on, and her survival rate was still much higher. But, Jack had essentially no insulation and in the tests, his core temperature plummeted too quickly. In water that cold, you have to keep your organs out of the water to have any chance of survival. They would have had to sit up on top of the panel and they still would have been partially submerged, but not enough for Jack to die that quickly. It is possible he could have lived long enough for the boats to come back, but there was still the risk of him dying once they were picked up. This is backed by the fact there were several people who had died from hypothermia after being picked up by a lifeboat such as William Lyons and Sidney Siebert.
Third, Jack and Rose both would need the dexterity and warmth to continuously make these attempts until they both were on the panel without critical submersion.
Fourth, hypothermia was not properly understood back in 1912 (at least in the Western world of medicine, I cannot find much on other regions) and wasn't actually studied until about two decades after the sinking. So, knowing each step in order to survive may not have been common knowledge since the medical world itself hardly understood it beyond the basic, "if you're cold too long, it's bad for you and may cause death."
Fifth, and most importantly, Jack would have needed to have 100% certainty that him also being on that panel would not put Rose's life in danger. He had already lived, and she was only beginning to break free from her chains. He wanted her to experience a good life, no matter the cost to him.
In conclusion, Jack may have been able to survive. But, he was supposed to represent the real pain of the loss the real people of Titanic felt, to represent every man who knew he would die, but stayed on the ship as she sank to save as many women and children as possible. Jack was never meant to live in Cameron's story, because those men, women, and children didn't live on the Titanic. Loving someone does not mean you can save them from death.
Almost 1,500 people were lost, and most were men. Imagine over one thousand women waiting for their husbands to be plucked alive from the ocean, to come aboard the Carpathia or one day walk through the door to their home, only to likely never even see a body or any trace of them again.
We are supposed to feel that loss, so we do not forget the loss that truly happened.
If you're interested, check out the real stories of Titanic survivors, victims, and heroes:
The real story of a Chinese passenger, Fang Lang (Wing Sun Fong), who was on a table post-sinking long enough to be saved. This website, Encyclopedia Titanic, is a great resource on simple, direct information on the Titanic; a good start on the beginnings of research.
Experience witness testimonies and the inquiry that followed the sinking, as well as interviews with modern Titanic researchers with the Witness Titanic podcast. It is a modern inquiry of sorts trying to piece together fact from fiction of what really happened during the sinking.
If you're interested in educational videos on sinkings and information of not only the Titanic, but also other ships and maritime history, check out Oceanliner Designs and Historic Travels.
If you have a favorite content creator who posts Titanic and/or maritime videos, drop them in the replies!