Short answer: no.
A coin dealer cannot be the custodian of your IRA. The law does not allow it, and the reason is worth about twenty minutes of your attention, because it explains almost every bad outcome in this industry.
But the interesting part is not the rule. It is how close some arrangements get to breaking it while staying technically legal.
A dealer can refer you to a custodian. A dealer can own a custodian. A dealer can coordinate everything so completely that you never speak to the custodian at all.
None of that is illegal. All of it removes the protection the rule was designed to create.
So the real question is not "can my dealer be my custodian." It is "how separate are these companies actually, and does that separation still do anything for me."