PCAOB audits are not required for your Tier 2 Regulation A offering, and of course, no audit is required for Tier 1 offerings (although some States do require an audit, they do not require PCAOB). 

However, PCAOB level audits are required to stay listed on the major two exchanges (NASDAQ, NYSE). For a Reg A+ IPO to the major exchanges, the offering starts as a simple Reg A+ and then is changed at the time of listing to be an S-1 IPO. For these IPOs, companies will be required to file PCAOB audits only AFTER they have listed. Not before. 

Note that listing your company via Reg A+ on the OTCQB or OTCQX does not require PCAOB. In this case, the audit obligation is the same as for the Tier 2 Reg A+ – once per year US-GAAP. This is a significant advantage for companies that used Reg A+ to list on these exchanges.

PCAOB audits are far more expensive than US-GAAP audits.