Probably not - it seemed to be just the effect of being in Azkaban.
It seems most likely that it was the effect of being in Azkaban. Sirius told Harry that Barty Crouch Jr. died in Azkaban, and that many others did as well. He also said Barty Crouch Jr. looked sickly when he arrived in Azkaban, but whether that was due to a separate illness is never mentioned.
“No,’ said Sirius dully. ‘No, he’s not in there any more. He died about a year after they brought him in.’
“He died?’
‘He wasn’t the only one,’ said Sirius bitterly. ‘Most go mad in there, and plenty stop eating in the end. They lose the will to live. You could always tell when a death was coming, because the Dementors could sense it, they got excited. That boy looked pretty sickly when he arrived.”
- Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot Returns)
During a portion of the time while Sirius would have thought Barty Crouch Jr. was in Azkaban, it was actually his mother taking Polyjuice Potion. However, on the first day he was brought in, he certainly wouldn’t have been switched out for his mother, and he seemed to be already affected by being in Azkaban. In addition, he said Winky had nursed him back to health, which wouldn’t be possible if he had a preexisting illness that would be terminal in the wizarding world.
“The house-elf nursed me back to health. Then I had to be concealed. I had to be controlled. My father had to use a number of spells to subdue me. When I had recovered my strength, I thought only of finding my master … of returning to his service.”
- Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot Returns)
Barty Crouch Jr. seems to have healed fully after being taken care of, which wouldn’t be possible if he was dying of a terminal illness. From this, we also know it wasn’t just the effect of taking his mother’s form, since then he wouldn’t need to be nursed back to health. He’d just immediately become healthy again when the Polyjuice Potion wore off.
It seems the most logical conclusion that being in Azkaban was sapping his strength and will to live, and would have been deadly for Barty Crouch Jr. had he stayed. Some people survived being in Azkaban (like Bellatrix, who was imprisoned there for fourteen years and wasn’t sickly when she got out), but many people died from its effects on them. Sirius said Barty Crouch Jr. looked sickly when he came in and started screaming for his mother by the first night - he didn’t seem to be the sort that could survive Azkaban. Once he got out, he escaped the conditions that were killing him, and with care from Winky, he was restored to good health. The “illness” caused by being in Azkaban was cured.