A few considerations here. First, if they pay about $1 CPC in their niche a $500/month budget can go pretty far. If they pay $25 CPC obviously not so much. That’s the first consideration when evaluating whether a budget is appropriate.
Assuming it’s somewhere in the middle you next have to look at what the expected conversion rate is going to be. If it’s very low it’ll be extremely difficult to optimize the campaign in any reasonable timeframe.
But let’s say it is $1 CPC and a 5% conversion rate is expected. That’s 25 conversions per month… perfectly fine budget.
Is more better, yes to an extent because you can obviously optimize faster. But when your budget is too large for your niche you end up spending a much higher CPA.