leeneia, I don't know enough about the variations in anatomy to speak for everyone, but generally no, don't close that space for any sound when singing. Not even to breathe.

One way to think of it: In that big space you made to air out the hot food, mentally place a raw egg (not a free-range sturdy egg but a mass-produced thin shelled egg). Now relax all muscles not needed to keep the egg whole and say those consonants g, k, r without breaking it.

Mechanics: When speaking, g and k sounds can be made by touching the back of the tongue to either the soft or hard palate. When singing with a raised soft palate--when singing with a mouthful of hot food--that palate is too far away to be reached by the back tongue, unless you lower it and break the egg. (Yechhh!) Instead, sound the consonants by touching back tongue to the hard palate (roof of mouth).
      When speaking English, non-rolled r sounds are made by touching both sides of the back tongue lightly along any of the molars or even further back, on the soft palate. However, when singing with a mouthful of hot food, that palate is out of reach, and if you don't want to break the imaginary egg, you'll form the r against the foremost teeth your back tongue can reach without tension. The rear-placed r is called a swallowed r. People use it a lot to hold a note instead of holding the vowel ahead of it and adding the r just at the last moment. It doesn't carry or blend well.

It takes time and extra muscle to constantly raise and lower the soft palate. To demonstrate for yourself, try to sing "Good, good, good, good vibrations..." while having your soft palate raised for the oo and lowered (so your back tongue can touch it) for the g sound. Do it slowly at first to make sure your palate is down for the k, up for the oo. Try it spoken and sung. Do you find it takes a lot of effort? I sure do! Worse yet, the imaginary egg is now slithering throughout my mouth and throat with bits of broken shell in the mix. (Ewww!)
      Try the same phrase with the imaginary raw egg (whole again) in place, and with the g sound made by touching the hard roof of the mouth. The choice to place consonants further forward allows much less tension and fatigue. The work to move the palate up, down, up, down is tiring. Most people will stop raising the palate if they place their consonants further back; it's too much wasted effort to do otherwise.

To test r, "Row, row, row your boat" works well.

I hope that helps.

While I'm on a roll: Another sound people often make with a horizontal-flat mouth (no raised palate) is ee. To sing a great ee, first get the mouthful of hot food and place the raw egg. Next, send most of your lip muscles and all your cheek and jaw muscles on a little vacation. Back tongue is the only muscle needed to shape and say (or sing) ee, and yes a little lip, just enough to open and let the sound out. Whatever distance your jaw drops when the muscles are off duty often allows enough space between the front teeth for the sound to emerge, but experiment by opening the jaw more and more, until it no longer sounds like ee, then go back to where it sounds right--that's a great basis for a wonderful ee. See Don Firth's post and a voice teacher about placement to make it excellent.