Have not tried Seafoam, but I did squirt brake cleaner down the pickup when I had it out. I never actually checked to make sure the tube was completely open but the brake cleaner ran through easily in both directions and the screen was clean when I took it out.
Also, I found the source of the rattling noise. I used a long wooden dowel as a "stethoscope" and tracked it down to the A/C tensioner. I saw another thread on this site discussing this issue. Now I just have to figure out if it was just the tensioner, the clutch, or the compressor. In my case it was louder with the A/C off and got better with it on. Later in the day it threw the belt so something stopped turning. Never squealed, just rattled.
The fun never stops!