Not really. 95% of the gas fees get burned and do not go to the validators at all. Only the 'tip' or 'priority fee' goes to the validators and even that is barely anything. Most of the transaction related income validators get is from MEV - basically bribes to order transactions in the block in a particular manner allowing arbitrageurs to extract additional value. These bribes are somewhat correlated to the level of the gas fees, but not always.