Will a campaign budget override the budget of the group it belongs to? What about Traffic Sources and Campaigns?

No. All items are bound by the budgets set on their ancestors in the tree structure.

This means that even if you specify a higher budget for it, a campaign will never spend more than it is allocated for the group it belongs to.

The same is true with Traffic Sources. You can allocate a budget for a specific Traffic Source that is higher than the campaign's budget or than the campaign group's budget but the campaign will simply stop running once its budget is reached.