Will my client actually see the same fonts I picked?

Not dumb at all, it's the right thing to ask. When you pick a local font like Calibri (or Arial, Georgia, Times New Roman, etc.) it gets embedded in the exported PDF, and it renders identically to what you saw on the canvas. Your client opens it and sees your Calibri regardless of what's installed on their end.

The substitution thing only kicks in the other direction, if you import a document that references a font you don't have, it gets a metric-compatible stand-in so the line breaks and spacing stay put. For a quote you're authoring in Calibri, you're covered.