You get a normal engineer, and he does in fact generate GPP points.
And actually, yes, the farms earlier is a pretty big help. Consider this:
2 Farms will had +4 food (With agriculture on grasslands or floodplains).
Engineer adds +2 Production
Great enginer (Turn 25) adds +3 production
When you build a settler, you'll have +9 production to do so, of which 4 of that is from just a pair of farms. I'll often have 3 or 4 farms, making this a potential of +13. However, you say that you can build that Mud Golem in only slightly less time. I think the actual time discrepency is pretty big. MG's cost 100 hammers. Even with that first Engineer specialist, it generally takes me 20 to 30 turns to build the first golem. At that point I've produced via the engineer 50 (Average of 20-30 *2) production, half of what was needed. You build farms in 5 turns(FloodPlain, 4 on grassland or plains), and I'm guessing most starts will have you taking another 15 turns to finish that golem, at which point the original golem will be finished farming, and your city will have grown to size 6 faster because of it. You'll also have a pair of warriors, and will have started on your first settler, reaping all the listed benefits.
Since growth in this game is exponential (Or a coefficient off from it) getting an early absolute boost is pretty big.