Does a bad fuel pump thow a code?
 

Or are there any other codes thrown due to a bad fuel pump?

Generally no, I don't believe the FP is connected into the OBD system. Mainly to determine fault you'd have to check for fuel rail pressure, power at the connector, and listening to see if it primes.

As you have an '03, if your FP died it may have been due to a clogged fuel filter in the sending unit (integral). I had that happen to me, went through several new pumps before I took the sending unit apart.

This is very general and may not pertain to Porsches/Boxsters, but a bad fuel pump can cause a lean condition that would trigger a CEL. Do you have a CEL, and if so, what is it?

When my fuel pump started to fail, there were no Check Engine lights or error codes.

On most cars a solid check engine light means something is not working that effects the emissions of the car.

When mine went there was a loss of power and an unwillingness to rev. No check engine light but two codes pertaining to a lean running condition. The loss of power was intermittent.

I have an intermitent SAI code. The car generally runs strong when first started and may run strong when hot or may refuse to rev above 3500 or stay running below 2000. It may behave and run perfectly as well. It's a whole new experience every time I drive it. I have cleared the SAI and it stays gone for a short period then reappears even when the ambient temp stays above eighty degrees.

For the SAI code, follow the lines. I had the small check valve break off and was not actually putting the air into the plenum. It threw the code sometimes, and sometimes not.

The SAI only works for a limited time after a cold start- no?
After I removed my FP I put power to it while it sat on the ground and it whirled intermittently- in the process of seizing. Fuel pressure? If it's the pump it's strange that there's no lean codes...

When my fuel pump went, there were no codes. Just stalled while doing about 65mph on the freeway.