It's safe to say that the Cell Saga was a major turning point for the Dragon Ball series. It introduced fans to the Androids, for one, the most terrifying one being Cell. Created by Dr. Gero, he possesses DNA from Goku, Vegeta, Frieza, King Cold and Piccolo. He was designed to be the perfect fighter and proves to be one of the strongest foes that the heroes face.
He even has his own transformations, a trait he gained from his Saiyan genetics, able to go the android equivalent of Super Saiyan in his Perfect form. With this in mind, could Cell also have an equivalent to Frieza's Gold Form?
In his Imperfect Form and Semi-Perfect Forms, Cell is able to absorb other living things and increase his strength via osmosis, dramatically surpassing his previous forms. He absorbed Android 17 to surpass his Imperfect Form, and Android 18 to his Semi-Perfect Form. On top of this, he's able to achieve a Super Saiyan-like form because, when he was created, Dr. Gero used DNA he'd collected from Vegeta and Goku. Cell is also shown to take on certain personality traits from his genetic parents as well, like Goku's laid-back personality or Frieza's pompousness.
Cell's ability to achieve Super Saiyan-levels of power was inherent to the DNA he'd received from Goku and Vegeta. But, at the time Frieza had yet to achieve his Golden Form. But that doesn't necessarily exclude Cell from potentially being able to unlock it himself. Frieza hadn't trained before his fight with Goku because he was a prodigy with a strength unlike anyone else in the universe, even his own family.
So, after his defeat, he trained intensely for a relatively brief period and was able to achieve a new power level -- one that even surpasses Goku and Vegeta's Super Saiyan Blue. But he had to put in effort in order to achieve it.
Because Cell has Frieza's DNA, it is theoretically possible for him to achieve this form. To do this, he would need to train his body to the point that Frieza did. He never actually trains at any point in the original series; instead, absorbing others to increase his power. Cell never pushed himself because thought he was above it. He relied on the boost he received from the Androids and then just stood around waiting for the Cell Games to begin.
In order for Cell to surpass his strength at the time of his death, he would need to go through the same training Frieza did if he were to try and go Golden. As a full-on android, Cell was programmed to follow certain directives (absorb the other Androids, kill Goku, etc.) and thus likely never thought about training. Beyond that, he was already "Perfect," so why bother?
Once Cell reaches his Perfect Form, he's shown to gain a bit more self-awareness and to be able to think for himself. Up until this point, it probably wouldn't be possible for him to reach Golden Form -- in a mentality sense -- because he was so focused on his original directives. He likely didn't have the capability to recognize that training would also help him become stronger. In order for him to reach Golden Form, Cell would need to have achieved Perfect Form first, meaning he'd still need to absorb everyone he did in DBZ.
It wouldn't be until then that Cell would have a fitting jumping-off point to reach Frieza's level. The only thing that would stand in his way would be his perfectly massive ego.