Source rock thickness is definitely impact the amount of HC generation in direct way, but the most crutial parameter is amount of organic matter contatained in source rock. Say if organic content is constant- the more thickness the more HC generation.
Thinking of source rock thickess and migration path- not sure it will depends.
The thickness of the source rock has no relation to hydrocarbon generation. The hydrocarbon generation is depended on TOC, maturity, enough maturity from depth of burial and thermal point of view, and reservoir rock associated with source rock. The thickness of source rock is important from the amount generated and expelled hydrocarbon.
I agree with Mohammad. The type, TOC percentages and maturation histories are extremely important. However, the largest the volume of the source rock the largest is, in principle, the volume of kerogen capable of producing oil and gas. It might also signify a more 'predictable' distribution of source rock through your basin, minimising risk.
Indeed, as Tiago and the rest have said, SR thickness and TOC is for sure important parameters that define the volume of generated hydrocarbons. Adding to these parameters you have to take in account the Hydrogen Index (HI). Not all the kerogen in SR's can be converted into hydrocarbons. There will be an inert carbon part remaining by the end of generation. The labile composition (organic matter) gets converted into oil or gas. and this is measured by the HI parameter (S2/TOC).
High HI produce more volumes of hydrocarbons, so this parameter, TOC and effective SR thickness have to be considered together when assessing the amount of generated HC's.
Migration (expulsion) would be a different subject not directly linked to this, except if you're referring to primary migration (the one that occurs within the SR, on the onset of HC generation)