After doing a bit of research, it seems that these combinations actually do have an in-game effect. What I noticed is that "good" character combinations light up more dots next to the three icons seen above the team name.
I tried playing a few matches against myself in order to figure out just what each of these icons mean (since, surprisingly, that's not written in the game manual) and was very happy to see that someone has done that work for me:
The first icon is a measure of how
much extra damage your TEAM ultimate
jutsu does. I believe 6 dots is a full
bar of damage.
The second bar is a measure of how
much faster your support characters
can be used again. I am not sure
exactly how much faster it is.
However, if you try out the Kakashi
and Minato combo (which has 6 dots in
this category) since only selecting
one support already lets you use that
support character 2x as much, your
gonna get to call Minato every other
The third and last column, is a
measure of how fast your team gauge
charges. Every time you call your
support character in, this gauge
charges a little (this is constant).
When ever your support characters
successfully hit or preform their
secondary roll (such as shuriken
support for balance, combos and hit
backs for attack types) the bar
charges more (I'm not sure how the
defense type gets more gauge though).
How much more gauge they get from this
is based on this stat. If you have the
Lee/Guy combo (which is 6 dots in this
category). Every time Guy hits with
his attack, your gauge charges a half
of one bar! Meaning if you hit with
him four consecutive times, then you
get you team ultimate!
So it seems that picking meaningful character combinations is a good idea, as it will give you a definite edge when using your support.