Is there any connection between "to stave off a cold" and a "barrel stave"?

Here's what etymonline.com has to say:

stave (n.)
"piece of a barrel," 1750, back-formation from staves (1398), plural of staff (cf. leaves/leaf), possibly from O.E., but not recorded there. The verb (to stave in, past tense stove) is c.1595, originally nautical, on notion of bashing in the staves of a cask and letting out the contents; stave off (c.1624) is lit. "keep off with a staff," as of dogs.

From what I can find out, yes, but I think you already knew that.

Staff was first attested by the OED c725, meaning "A stick carried in the hand as an aid in walking or climbing." The plural of staff (with this meaning) is staffs or staves.

Stave, meaning "Each of the thin, narrow, shaped pieces of wood which, when placed together side by side and hooped, collectively form the side of a cask, tub or similar vessel," is a backformation from staves and is recorded by the OED from 1398: "A tonne is an holowe vessel made of many bordes and tonne staues craftly bounde togyder." (Stave, meaning "A rung (of a ladder); a cross-bar to the legs of a chair," is attested from c1175, though the first one in a language I can understand is from a1825: Stave, a step or round of a ladder.")

Stave, the verb meaning "To break up (a cask) into staves; to break into and let out the contents," is recorded from c1595: "A bark..beinge forst to cast overborde all..theire fish and to stave theire caske in the whiche theire fresh water was."

Dictionary.com - staff

Dictionary.com - stave

Online Etymology Dictionary - stave

By the way, I mistakenly thought the a before a date meant about or around. It means ante (before). I was right about the c, though. It means circa (about).