The base coat before the greying process begins does not determine if the are flea bitten or not. I was raised with many grey foals. Only one of them was really flea bitten, and she was showing her flea bites before she got to a light grey.
For example, here is a gelding that was born dark chestnut, no flea bites ;)
He is a heterozygous grey, one grey (non flea bitten) parent
Here is his full sister (born chestnut):
She had a very few, scattered flea bitten spots that were hard to find.
Their little half sister (also born chestnut) who had a very flea bitten heterozygous grey sire:
She had her flea bitten marks showing up by the time she was three years old.
It is a case by case basis if they are flea bitten or not. I haven't seen any greys that have solid black base coat get flea bitten, but have seen some chestnut and bay based greys end up being flea bitten. But not all chestnut and bay based greys end up being flea bitten. I would consider it more likely to occur if the grey parent is flea bitten