It does not. Also, this thread is labeled G&K, so you can ignore references to Great Musicians and Writers, since they are BNW only.
The faith cost of Great Persons in both G&K and BNW is completely unrelated to the Great Person Point cost of Great Persons (i.e., "regular" Great Persons). At Standard speed, the cost of each type of Great Person starts at 1000 faith, and increments in multiples of 500 for each subsequent GP of that type --- so the faith cost of GSs goes from 1000, to 1500 (+500), to 2500 (+1000), to 4000 (+1500), etc. and the increment for GEs is the same, regardless of how many GSs you buy.
And none of those faith purchases has any effect on the Great Person Point (GPP) cost of "regular" Great Persons, where the GPP cost increments by 100 (at Standard speed) for each generated Great Person (100 GPP, 200 GPP, 300 GPP, etc.).
In G&K, the main complication is that GSs, GEs, GMs and GAs were all on the same GPP counter, so a Great Artist , for example, would increase the GPP cost of the next GS/GE/GM/GA by 100 points. In BNW, Great Artists were moved to their own counter, so now only GSs, GEs and GMs remain on the common GPP counter (and the new BNW Great Persons -- Great Writers and Great Musicians -- are also on their own separate counters).