Albino and Pied are both considered recessive AND they are proven to be different genes. So while the homozygous albino would for sure give the albino mutant version of the albino gene to the offspring and the homozygous piebald would for sure give the piebald mutant version of the piebald gene to the offspring they would each give the normal version of the other gene. You would end up with normal looking double hets. Actually, you might see some striping in the belly pattern due to the single copy of the piebald mutation but some het pieds don't show that (and some normals do) and you would already know they where het pied anyway.
Now if you bred a het pied to a homozygous albino all the babies would be het albino but would only have a 50% chance of being het for piebald. That is where looking at the belies might help you pick out the het pieds but it’s not a sure thing.
The next generation when breeding the double hets together is when each egg would have a 1 in 16 chance of being an albino piebald (which has been produced).