There is a limit on pirate upgrades, but it's way high. Here are the numbers:
Pirates buy 2 upgrades before each raid, each of the following upgrades has 20 ranks:
Armor: +2 armor.
HP: +20% hp.
Regeneration: +45% hp regen.
Weapon damage: +20% damage, +5% range.
Weapon cooldown: -7% autocannon/laser cooldown.
So, basically, you have pirates running around with +40 armor, +400% hp, doing +400% damage with double the range and virtually no cooldown and with 900% faster hull regen.
Granted it takes some time for all of these to build up, but since they're random they could well end up with a 40% damage bonus and +10% range on the first raid and only get worse from there.