No, in fact you're likely a distinct disadvantage, but game theory comes into play here.
When teams A and B play, they are almost certainly going to each pitch their best starter in the game. If A wins, they are pitching their #2 starter vs C's #1.
Because home field advantage in baseball isn't a strong indicator of success Home teams only win about 54% of their games (same in postseason and regular season) at home. However, usually teams match up their best starters against each other in a playoff series.
So the first game favors team A by about 4%. Team C is going to have an advantage in the second game, even though they are the away team, because their #1 gets to go against the #2 of the team that won. Depending on the quality of team A's #2 starter, this may give team B enough of an edge to at least turn the game into a coinflip affair.
However, there is an additional consideration here. It's all about how much time passes between the tiebreaker game and the start of the first playoff series (or the wild card game). Team C might look at the matchup, and run out their #2 having confidence that he can beat the other team's #2 and save their rotation from getting out of whack in the first playoff series. This is a game theory decision and should be informed by way more math than I can pack into this little post (at least without running on for several pages and doing a lot more research that's not directly relevant here). If this happens, and we assume that #2 starters are equivalent, we're back to that 54% edge for the home team.
So, depending on how much of an impact you believe starting pitchers have on the outcome of a game (I tend to think it's a fair amount), the tie breaker situation either favors team C, but not by very much, or team A, but again, not by very much.
The reality is that playoff baseball is a crapshoot.