If plants have more fertilizers does that mean the rate of photosynthesis increases for the plants? ?

Question

or will they photosynthesis more than usual

Answer 1

Only indirectly.  Photosynthesis is when water and CO2 are combined to produce carbohydrates and oxygen using light energy captured by chlorophyll in the plant's leaves. Fertilizers provide the nutrients for plant growth, so more fertilizer over time could result in more leaves being produced, so it *could* result in increased photosynthesis only because the plant would have more leaves.  It wouldn't affect the rate of photosynthesis at all - this would be controlled by light intensity and day length, and water availability (if conditions are dry, the stoma may close to conserve water which also reduces CO2 absorption).  

Answer 2

No. It means that the plants are given the vital nutrients that help them grow quicker, like a vitamin.