First of all..... I got the impression there was to be 2 posts with a sign, not one post per sign. Anyway, where was it mentioned he was going to be putting a metal stake inside it ?? I thought he wanted to know if he could just use the sleeve ?? You mentioned it, but how far in the ground do those stakes go ??
Yes, he asked about setting PVC post sleeves in the ground. I doubt he'd be using two 4.25"x4.25" posts for a single 18x24. That would look really strange. Way too thick legs for a sign that small.
What I suggested was buying a system made for doing exactly what he wants to do, one which obviates the need for digging 3' holes in front of every house for no good reason. Price-wise, it is favorable to the cost of buying post covers at the local home improvement store. If you would spend just 60 seconds browsing the vendor's website, you'd see that the stakes come in two lengths. The standard goes 18" into the ground, and there is a portion welded to the stake above ground that goes up into the post. This is from a vinyl post and panel company which also sells frames.