Will a copyeditor refine both dialogue and plot?

Generally, no.

The traditional editing process has three layers. In order, there's the substantive edit, the line edit, and the proofread. All three require a different set of skills.

The substantive edit (this process goes by a number of different names) aims to address 'big-picture' elements such as plot holes, character arcs, pacing, etcetera. When the substantive editor is done, your manuscript will be returned with a whole lot of red lines suggesting you cut out the car ride to work and the protagonist's extensive ten-page morning ritual. Annotations written in comment bubbles will point out where your characters come off as unfeeling wooden blocks or as reptiles in human skinsuits.

The line editor is, as the name suggests, concerned about your story at the sentence level. Expect a returned manuscript in which all clichés like the phrase "like a knife through butter" are highlighted, as well as suggestions on where to break up run-on sentences and where to improve sections written in passive voice.

Finally there's the proofreader, who has your manuscript open on one side and Strunk and White on the other. The proofreader catches grammatical errors, like sentences in which you forgot to modify the verb for the subjunctive mood, and similar subjects such as punctuation. Of the three, this is the most 'objective' form of editing.

You might find an editor who will do all three. But not as a 'package deal,' for the simple reason it makes little sense to correct a misspelling on page three if it's uncertain whether the encapsulating scene will make it through to the next draft.