My girlfriend's father helped me install a new water heater, and I watched
closely in the interest of eventually being able to do something my darned
self someday. Well, it turns out my chance came sooner than I thought. The
pipe feeding cold water to the tank has a slow leak at one of the connectors
(copper pipe fitted to another copper pipe). Looking at it closely, it
doesn't have the silveryness of the other connections, so maybe we forgot to
solder it, but it's such a slow leak that this seems unlikely.

Anyway, the leak is from the BOTTOM of the connection, so if I want to fx
this without cutting pipe and dismantling everything all over again, the
solder would have to suck upwards into the joint. So my questions a

1) with a cutoff valve being right above where this leak is, can I assume
that shutting it off and draining the water heater a little bit will give me
a water-free inside of the pipe at that point so I can successfully heat up
the pipe enough for solder?

2) Assuming "yes" to the above, will solder flow upwards into this joint,
"sucked" up by the heat?

Thanks for any input here, I'm a floundering newbie. I appreciate your
time.