You need to define what you mean by "metabolism."
The article you link seems to be discussing how well your body can extract energy from food, not how "efficiently" it uses that energy, so there is a bit of ambiguity.
Would it allow them to go for weeks without air or food?
The short answer is yes and no, if your aliens can extract energy from food more efficiently, then they require less of that food. However, it's not that they're burning fewer calories; they're just getting more from the same amount of food. So then for air? The answer is no. There is a difference in extracting calories from food and using those calories. If we're saying digestive efficiency is higher here, being able to extract calories from food more efficiently doesn't mean your alien's metabolism rate is lower; your alien still needs the same amount of oxygen to properly burn the calories in the food it takes in.
Personally, I find this answer to be a bit boring, so let's delve deeper into other ways your alien can have a "more efficient metabolism" and what they mean.
True Metabolic Efficiency
A concept of "true" metabolic efficiency would mean that your alien is able to use less energy to power its biology. And when it comes to powering biology, obviously we're going to be talking about mitochondria. In all eukaryotic metabolism, glucose is used to power the creation of ATP. The ATP is then used to power the structures of the cell. This happens through glycolysis and the citric acid cycle. Oxygen is used to essentially "burn" the glucose and produce NADH and pyruvate, which are used by the mitochondria to power molecular pumps. These pumps move protons between the membranes of the mitochondria to create a charge differential. This charge differential them moves electrons in the electron transport chain, which essentially uses electricity to power cellular machinery that assembles ATP. Since ATP acts as energy storage, you can think of all this grand machinery as a simple way of charging tiny biological batteries. It's a bit more complex than this, but for our purposes this explanation is sufficient.
Now, if you increase the efficiency of the electron transport chain, you're able to assemble more ATP with less input. Unfortunately, this chain is already pretty efficient since it's had 4 billion years to perfect, but for world building purposes let's go all Jeff Goldblum here and assume "life has found a way."
What would it mean if this electron transport chain, or indeed the mitochondria as a whole, is more efficient than that of a human? Well, we already have some biological examples: birds.
Birds already have more efficient mitochondria than humans, and it leads to a lot of interesting effects.
Mitochondrial processes are the prime source of oxidative stress, which causes damage to the cell, and is a main contributor to aging. Oxygen is a very nasty chemical; it's quite reactive, and its greek name means "acid maker." Our cells are using it to literally burn glucose, but it cuts both ways: the oxygen can burn the cell itself and cause damage. This is because waste products and intermediary products called free radicals leak out of the mitochondria as part of its normal metabolic processes. The cell has to spend energy neutralizing the free radicals and repairing damage from them, which all effects efficiency. Mitochondria in birds are more efficient, and produce far less of the waste products and free radicals that cause this damage in the first place. The result? Birds have extraordinarily long life-spans for creatures their size. For example, the african grey parrot and macaw both have lifespans on the order of 60 years, despite being warm blooded with high metabolic rates. You'd be hard pressed to find a mammal of similar size that lives as long.
Birds also process oxygen much more efficiently than mammals. Although this is due mostly to the way their lungs are constructed, their highly efficient mitochondria no doubt also play a role.
So, to answer your question, if you want your aliens to have a truly more efficient metabolism, say their mitochondria (or whatever equivalent organelle) are highly efficient.
In this particular case, you might even be able to say they can go a long time without air. Probably not weeks, but definitely longer than a creature of the same size and metabolic rate.
You could say they process glucose more efficiently, and their molecular pumps and the electron transport chain are much more efficient. In this case, yes, they could go a long time without food. You could even throw in better digestive efficiency to make them extract more calories from their food as well for an even bigger punch.
In addition, because their mitochondria are super efficient, they would likely live much longer. A human with bird mitochondria might actually live for 200 years or more, so you could say your aliens live for a very long time.