Not according to the official NASA history, On the Shoulders of Titans.
White had difficulty opening the hatch to start the EVA:
Over the Indian Ocean, White was ready for EVA at last - hoses hooked up, umbilical ready, gun in hand, and chestpack in place - and they again rested and chatted. Nearing Carnarvon, Australia, they began to depressurize the cabin. Then a mechanical problem arose - the door would not unlatch because a spring had failed to compress. After much yanking and poking around the hatch ratchet, the door suddenly cracked open. White found the hatch as hard to push up in zero g as it had been on the ground.
and closing that same hatch at the end of the EVA:
White closed the hatch and reached for the handle to lock it. When it failed to catch, he knew it was going to be as hard to close as it had been to open. Pushing on the handle lifted White out of his seat, so McDivitt pulled on him to give him some leverage. Finally White felt a little torque in the handle and yelled for McDivitt to yank harder. The door was latched.
But this was a mechanical problem with the hatch, and had nothing to do with the pressure of the spacesuit.
He had no trouble getting back in to the capsule:
Finally, after 15 minutes 40 seconds, McDivitt broke off to ask the ground if they wanted anything. "Yes," Kraft chuckled, "Tell him to get back in." After he passed this on to White, McDivitt heard boots thumping atop the spacecraft. White came back to the hatch as Gemini IV was passing over the Atlantic, dismounted the camera and removed electrical connections, and handed all these items to McDivitt along with the gun. McDivitt then helped White get settled, pulling on his legs and guiding his feet into the footwells.
After the hatch was closed, both astronauts were exhausted. They rested in their spacesuits for almost one orbit, before bothering to repressurize the spacecraft:
White sat back, physically exhausted, sweat streaming into his eyes and fogging his faceplate. McDivitt also felt tired, so they rested before extending a radio antenna to find a ground-based voice and tell Earth all was well. Carnarvon answered them. The crew of Gemini IV had almost circled the globe in an unpressurized spacecraft.
Perhaps this last part was somehow misinterpreted into the incorrect story of White depressurizing his suit.