Great question, however hard it may be to provide a satisfactory answer to... :)
I cannot give you statistics on homegrown vs foreign managers in national teams, but I just want to point out that there are lots of homegrown managers that do not do well at all, likewise foreign managers that do wonders. Let's look at some examples:
Brazil won all their World Cup titles with Brazilian managers, even when they came 2nd or 3rd they had Brazilian managers. For that matter, I don't know if they ever had a foreign manager, and it appears as if it hasn't been much of a problem for them.
Italy, much like Brazil, won all their titles, got 2nd and 3rd place finishes in the World Cup with Italian managers.
Germany, again like Italy and Brazil, got to all her top three finishes in the world cup under the leadership of German managers.
The same pattern applies for France and Argentina (possibly with other nations). For instance the Turkish national team had breakthroughs only when they had Turkish managers. On the other hand Greece had her breakthrough under the management of Otto Rehhagel, a German manager, during which they won the Euro 2004: beating the host nation (Portugal), the title holders (France) and the the popular favorite (Czech Rep.).
Likewise Russia had a great streak of international success, first with Guus Hiddink and then now with Dirk Advocaat, both are Dutch. I do not recall any major success from the Russian national team with a Russian manager leading the team.
It's hard to give a definitive answer to this question but I'd say if you consider World Cup to be a good enough measure for success for national teams, then I'd say the scales are definitely more towards the home-grown coaches, which to me is not such a surprising insight. Coaching/managing national teams is tricky, players do not get to play with one another that often, there might be strong rivalries between them (e.g. England, Spain) the schedules might be challenging... It's important for the manager to find some common ground for the players to unite around, and be able to motivate them when they are down or confused, shake them to their senses when they are lazy or complacent. I believe a lot of those common grounds, values lie within the cultural codes of the upbringing in a nation and language. A foreign coach might benefit a national team in many ways, however in times of need it's more likely that a homeborn manager will come through for them.
Hope it helps answer your question