The most important part of senji from my experience was the ability to attack. Unlike a normal area of control game where the primary purpose of troops is to conquer territories, in Senji the primary purpose of soldiers from a time perspective is to die in combat thus gaining you honor. While holding territories does give you more actions each turn, it also makes you more vulnerable to attack due to the very low piece limit on troops.
Naval attacks confer fairly low penalty compared to the high value of the attack opportunities they can create, so naval connectivity is usually the most interesting feature of territorial positions rather than land connectivity (another difference from other area of control games). As a result, black, yellow, and purple are in the more advantaged offensive positions in that they have starting territory on both seas, allowing them to attack almost any territory on the board (with the exception of the two inland territories controlled by red and green). Thus, if there is a tempting opportunity for combat (such as a situation where you can win a 6 on 5 battle), these players will almost certainly have it available, while other players only have a 50% chance that they will be able to get to that territory.
The check against this is that the seas go both ways: these players can also be attacked by anyone from pretty much anywhere. This is less valuable than in a classic are of control game, but attacking a player that has just taken a fourth territory can matter a lot.
Do they make a significant difference? Not when compared to games like Game of Thrones. I would say starting positions in Senji are more comparable to starting positions in classic Risk; they are not symmetric, but the map is connected enough that the asymmetry is merely enough to add nuance rather than throw off game balance.