Has this ever happened? Can it happen? I'm a novice in linguistics and I'm trying to study sound changes.
It depends on what you mean by "sound change", as distinct from "correspondence relationship". There is a general analytic framework set forth in R. Kirchner's dissertation that explains the individual steps in lenitions, and I think it is quite applicable to these phenomena. As an example, a number of languages of Cameroon and Nigeria (e.g. Beti-Fang language, Kenyang, Ibibio and Efik) seem to have intervocalic voicing + spirantization, which acts stem-medial stops (and apparently only stops). Closer scrutiny shows that actually there is a "shortening" of the consonant where closure duration is radically reduced – the initial impetus is something about rhythmic organization of speech. The appearance of voicing (and spirantization) involves secondary developments, with voicing "bleeding through" to the stop, and with incomplete closure owing to the very short time-slot allotted to the consonant. (In Ntumu and probably other languages, this in fact results in regular nasals becoming "fast" nasals). This rule in Ntumu does not affect final /s/.
If this is how "intervocalic voicing" develops generally, then correspondence relations like *p,t,k → b,d,g would have as the first step in the change *p,t,k → p̆,t̆,k̆ /V_V, then other phonetic processes contributing to a phonological correspondence of earlier p to later b. That is, "no, it can't happen" because the phonetic causes are more complex.
A complicating factor is knowing that you actually have voicing. Danish may have such a process: or it may not (is "b" [p] or [b]?).