I use the formula: 1-exp(-CDS*(1/LGD)...) to get implied PDs from CDS spreads. But what if the currency of the CDS is not USD? For instance, if Country A has currency that is 1000000 to 1 USD, that doesn't necessarily mean they are more likely to default. So, should the spread be converted to USD or not? Thanks!

How do you think the level of the currency of the CDS affects your calculation? Perhaps equivalently, what do you mean when you talk about converting the spread to USD? I am not saying that there isn't potentially an issue with your calculation when you look at CDS quotes in different currencies, but it has nothing to do with current exchange rate levels.

In the case of your simple formula there is no dependence on currency.If you use a regular vanilla CDS pricer in order to bootstrap a survival curve so as to match the market data inputs (either par spreads or fixed coupons + upfronts) then the discount factors from the IR curve feed into the price and consequently there is an IR dependency (albeit small for par CDS). As a consequence if you see CDS in different currencies marked at the same par spreads then there is an implied arb (although not necessarily one that is easy to capture in real life) since, as you say, the currency of the CDS should have no effect on the reference entity undergoing a default event.

There is a second effect, which is typically referred to as a quanto effect. While you can deliver bonds of any major currency into a standard CDS contract, the quantity of bonds delivered is determined by the notional in the contract currency and the exchange rate on the auction date (or the day before if memory serves me right). This is especially important for sovereign CDS, and we are seeing pretty substantial discounts offered if you buy protection on core Eurozone sovereigns denominated in EUR instead of USD (which is the standard), far beyond what can be explained by the difference in discount rates.