When a recipe asks to add spices to the oil, can you add the spices directly to the sauce for the same effect?

Fat transport the flavour. It is the one who get infused with the spice or herb. That's why flavoured oils are so popular, you add one thing instead of 2.

Think of making a hot oil. You heat up oil, add spaces and THEN use whole oil in whatever you want.

So adding spices later, to finished sauce may not bring all the taste out. It may be a little bland.

But what you can make is your own flavoured oil. Just use the amount required by the recipe and add different spices with different quantities. When the oil cool down use it in the final recipe.

The effect will be different for a few reasons.

1. When you add spices to hot oil, they cook at a considerably higher temperature (up to around 200°C) than in a simmering sauce (100°C as it's likely to be mostly water). Important cooking chemistry happens at this higher temperature, so the flavour is actually changed (just as with onions and garlic).

2. Whole or coarse spices sometimes pop and break up (I often add whole or lightly crushed cumin seeds to hot oil and fry, but if you add them after adding watery liquids they get stuck in your teeth). This can be mitigated by using finely crushed/ground spices.

3. Even if the oil is cold, many major flavour compounds are much more soluble in oil than water, capsaicin being a significant example. The flavour extraction will be affected. Taking chilli flakes as an example, you can add them later, even at the table, but the heat will be concentrated in the flakes; adding them at the beginning of cooking allows the flavour to infuse the whole dish. Again finer spices can help here by dispersing in the sauce.

On the other hand it's perfectly sensible to add black pepper to a simmering sauce, to taste. Turmeric is also often added towards the end of cooking as too much cooking removes some of the best elements of the flavour. Paprika is also sometimes added late (or even to the oil and at the end).

Bearing this in mind, experimenting is a good thing. If you put a baseline level of spice in the oil, you can get away with topping up the flavour, with a little care.

As other answers have noted, stirring spices into the nearly-finished dish will give a different taste because frying something in oil is physically and chemically very different from boiling it in water.

One possibility would be to use what in Indian cooking is called a tarka (and a hundred other names, too, depending on which part of the Indian subcontinent you're actually cooking in). Instead of just adding raw spices at the end of cooking, fry them in a little oil first. You can then add as much as you think is needed. The result won't be exactly the same as adding them at the start, but it will be a much better approximation.

Or, as Chris H suggests in a comment, if the recipe begins by frying spices in oil before adding other ingredients, you could start by making more of that than the recipe calls for, and reserve some to add later. That wouldn't work for recipes that, for example, involve frying onions and then adding spices.

According to Cook's Country / America's Test Kitchen, it depends on the spice (whether it dissolves in oil or water). If the recipe specifies adding to oil, adding it to the sauce (oil mixed with water) will reduce the flavour added.

Recipes usually specify things for a reason.

Adding clarification to the answer no.

Spices contain volatile oils, also called essential oils.

Volatily is a chemical identifier of a substance tendecy to vaporize.

Essential is a hundreds of years old, more subjective term, commonly used with spices and aromas such as perfumes. It refers to the essential aspect of any plant tissue. That what makes cinnema, cinnema. It's also an extraction method.

Conflating indicators aside, they are in fact not pure oils but aroma and flavor compounds setteled in resin acids and fat. They do however, have the same feature as oils, beeing fat-soluble and hydrophobic.

Fresh/dried/roasted/chooped, all methods effect and some strive to retain these "oils" that impacts flavour.

If the prepared spices you use has any of this "essential oils" left in them. The following argument has sicentific, chemical merit:

As oils disolves oil and volatile compounds are quantified by temperature, the release of flavor will be different at 200 degrees Celcius in oil as opposed to the non-solvent substance of water at 110 C.

Even a creamy sauce has alot more water in it than pure oil.

Some of these non-fried compounds will not be released in a typical sauce for many hours. If there is no fat or high temperature? Same outcome is impossible.

Keep in mind, blind tests on the most high minded paletts have proved time and time again that people have a hard time telling the difference between many methods. The difference could be neglectable to human sences.