If you're talking about the GoDaddy service, they're not. If you're talking about WHOIS privacy services in general, then possibly.
If you use a registrar's WHOIS privacy service, then the registrar still has the (supposedly) correct details and are simply masking them in WHOIS. There's no issue there. However, if you're not using the registrar's own WHOIS privacy service, then yeah, you're potentially opening yourself up to a world of pain, as (a) the domain is no longer actually registered to you in a manner verifiable to the registrar and (b) you might not be able to receive important notification emails that the registrar is required to send you (such as expiry notices).
