While the development of "modern" diplomacy might have started in the Italian city-states in the 14th century, I guess we'd be on safe ground if we agreed that under almost all conditions, the life of a non-aristocratic diplomat would have been most difficult.
First, remember that paid diplomats are a very recent innovation. The diplomat paid for himself, and that required rather more capital than was available to merchants. Italian merchant princes excepted.
Second, receiving countries paid the diplomats, not (as today) the sending ones. This lasted until well into the 17th century. The monies were paid in a mix of gifts and retainers. Nor surprisingly, they were closely correlated to rank.
Third, while the modern concept of "ambassador" is not strictly applicable in the EU3 timeframe, the idea that a mere merchant or clerk could represent a Crowned Head of State would have been risible. The Dutch, for example, had difficulty getting themselves taken as seriously as they ought to have been, mainly because they appeared too republican. As for the Swiss, did they even have regular embassies in this timeframe? I seem to remember that the Louis XIV kicked up an almighty fuss about receiving their envoys, as this as seen as simply too infra dig. (The Swiss, not surprisingly, tell that story differently.)
However, I do agree that a formal diplomatic corps thingy would be nice, late in the game. Maybe a special development you can build in your own capital that counteracts any ill effects from badboy or something?