It definitely plays in. Higher gravimetric or volumetric power density equates to higher stresses on various components.
Of course, just because your car offers xyz hp SAE Net, doesn't mean that it has ever actually put that out - so there are other aspects:
-engineering out stresses which can be done, but generally yields more expensive or larger components.
-actual power use, which trades lubricant, design, and actual use for lifetime. Some increased degradation may be acceptable in the name of other variables.
The other question becomes whether the increased power density is due to more fuel or better utilization of the fuel already being burned... that is, say you make 100HP in your engine. You are also making 200HP of waste heat, some of which gets loaded to the oil, driving viscosity down, then reducing the protection at the bearings that are taking the load from the power. Now, say instead, youre more EFFICIENT, so youre making 125hp, and only 175 hp worth of waste heat. Youre making more power, but the heat load on the oil is lower.
To the contrary, say your engine is efficient to the point where you are making 100hp and 200hp of waste heat. Say you change your fuel map, add a turbo, etc., and are now making 125 hp, but also 250 hp of waste heat. It then comes down to balancing longevity, parts sizes, etc. As specific power goes up, so parts and surfaces go down, you start to balance higher loads on the parts with lower viscosity in the lube oil (due to higher heat loads), and when it all comes together, you really need a heavier lubricant to offer the same protection.
A good example is the N54 3.0L twin turbo BMW engine. As an NA 230hp mill, it runs great and for a LONG time without issue. In the high-power version, youre seeing oil temperatures that take the engine into a limp-home mode.
So there are lots of variables, and my hokey examples only are a very small part of the story - there is lots left out here... but as a whole, Id say yes, higher the hp/l, particularly if YOU induced it, and not the manufacturer, the more the need for a viscous, robust oil.
