Gil, If I've read you right, and you've read me right, this means you have 8 downspouts connected to 4" corrugated pipes, which ALL connect into one 4" corrugated pipe before discharging to a swale?
If that's correct, you're asking for back-ups; one 4" corrugated line isn't large enough to handle the output from 8 downspouts in a good rain, let alone a heavy downpour.
Gil, the corrugated pipe will cause drag & turbulence in the flow of water, slowing it down. During average rains it will also "catch" debris & silt, which could clog or slow the flow even further. The Gutter Helmets will cut the debris to a minimum, but some will likely still occur.
This was also part of the reason I mentioned cleanouts earlier, and the concern of trees. The tree concern is two-fold here, because you not only have leaves to consider (which you've got pretty well covered), but you can also have rooting problems just like with a sewer line; any pipe below ground which does not have completely sealed joints will attract roots from trees, shrubs, grass, etc. and will eventually need to be snaked out.
Even it were smooth-walled S&D pipe, which would be my choice for this, your main line is undersized.
Determining the correct sizing depends primarily on 3 items; the length of guttering served by each downspout (to estimate the potential amount of water it will deliver), and the length of pipe from the downspout to the main distribution pipe, and the length of the distribution pipe going to the swale.
Hate to throw a wrench in the deal here, Gil, but want to be sure you're aware of the possibilities. Post back with some rough distances if you would, and let's see if breaking things up a little would be in order.