Please consider providing a little more context on what you're up to here, what or who you're protecting against, or what you've been asked to do here with encryption. Some additional background information might help folks better tailor an answer to your particular question.
By itself, a pgp key is small number of characters. A pgp key is a form of a digital certificate, and a fancy form of a password; a password with a number of additional features and capabilities.
If you use the pgp key or the digital certificate to encrypt or decrypt data stored on disk or sent over the network, yes, there is some computing overhead. While the encryption algorithms used are designed to be very efficient to encrypt and decrypt while also being very difficult to break, encryption is still added overhead.
As an example of encryption you're likely familiar with, the web https uses digital certificates, and encrypts and decrypts the network connections to protect against eavesdropping and injection attacks and (to a degree) spoofing.
With OS X, pgp is probably most commonly used with mail, and the overhead there is negligible. Encrypting and decrypting mail messages isn't a whole lot of data, and doesn't involve a whole lot of effort. You'll also need a pgp-capable mail client, as OS X mail doesn't support that. OS X mail does offer encryption capabilities using what's called X.509, but that's not compatible with the pgp encryption implementation.
You can see the X.509 digital certificates (keys) stored in your own OS X keychain and in the system keychains using the Keychain Assistant tool.
If you're encrypting and decrypting a whole lot of data, your Mac will be working harder.