Can I gain mass and muscle with gym and high calorie foods without any specific protein intake?Assuming you hit a minimum baseline of protein intake (approx. 0.8 grams of protein per kg of bodyweight) you certainly could gain muscle mass with a high caloric diet that focused on carbohydrates and fats instead.
It's just a considerably harder way to do it and your upper limit of development is probably lower. It wouldn't be advantageous and I'm not really sure why you'd even want to attempt such a feat. Unless you have a medical condition that interferes with protein absorption.
Damaging your body through high quality training requires repair, which requires an availability of amino acids for shuttling to repair sites. If you don't have those amino acids available your body will break down other tissues to manufacture them.
A higher protein intake is muscle preserving by nature, so when intakes are high you avoid this cycle of; Putting on a little mass; Training hard; Letting your body breakdown proteins from that reasonably new muscle; Hoping that the muscle you've repaired yields more than the muscle you potentially broke down.
That's why recommendations for athletes are typically a lot higher than general population. Athletes are advised to get 1.6-1.8 grams per kg of bodyweight in high quality protein (vs a minimum of 0.8 grams per kg from above - it's twice the intake), or more! If you're training hard in the gym 3-4 times a week or more, you certainly qualify as an athlete.
I use a range of 1.8-2.4 typically, particularly for muscle building objectives. Protein ingestion above 1.6 grams per kg, shows a considerable advantage in preserving lean muscle mass, but if you want to add muscle tissue then you probably want to slightly exceed that.
The other factor to consider is the metabolic effect of protein. High protein consumption is more metabolically active via digestion, so you need a higher intake typically than you might expect to counteract that.
A diet excessively high in carbohydrates and fats is more likely to result in fat storage over muscle development. What weight you do gain is far more likely to be fat, than muscle if protein intake is low. Unlike energy (ATP), which can be created via the breakdown of any of the macronutrients, your body can't really break down fats or carbohydrates for amino acids. Your body will have to pull them from tissues like bone or muscle if you don't have enough bioavailable. Using a diet higher in protein is more likely to result in desireable lean mass gain, vs fat mass gain because of free-floating amino acid availability.