Does it help to spread your debt across all your cards?

The short answer: Sometimes.

The long answer: The FICO scoring model considers utilization by looking at your balances divided by the credit limits on all your cards, as well as the single highest utilization on your credit cards. It's possible for two consumers owing the same amounts and having the same credit limits to get different credit scores if one puts a large balance on a card with a low limit, causing that card to have a high single utilization compared to the other consumer.

Spreading your debt across multiple cards generally won't help your credit score, unless putting all your charges on one card would put that card close to being maxed out.
Having one credit card with a low credit limit could harm your score if you charge up a high balance on it, but your score could also suffer if you charge high balances on all your cards. People with balances on a number of cards are more likely to mismanage their credit. As such, there can be an impact to your score of having a large number of credit cards that have high balances on them.

Good credit management will save you money and help you build a better credit score.