Yes—smudges and grease can make images look more flarey, but usually not by creating classic lens flare patterns.

Traditional lens flare is mainly caused by strong light reflecting between lens elements, often producing distinct bright spots, streaks, or shapes. Fingerprints, grease, and similar residue more often scatter light across the front surface, which tends to cause a hazy, veiled look, lowered contrast, and a glow around bright highlights rather than well-defined flare artifacts.

So the short answer is:

• greasy/smudged lens: more likely to cause overall clouding, softness, and glowing highlights
• internal reflections in the lens: more likely to cause classic flare spots/lines

This is similar to how smeared glasses produce glare and halos around lights. In fact, photographers have sometimes deliberately smeared material on a filter or lens to create a soft-focus glamour effect.

If you want the cleanest image and best contrast, keep the front element clean and use a lens hood or shade the lens from strong off-axis light.