With the older 5 pin MIDI, it's a minimum of about 3 msec between the time a MIDI Note On signal is sent and the time a note triggers. Could be longer using MIDI thru, poorly designed synths and patches, etc. But in normal use it's unnoticeable. With USB I suppose it could be less.
With MIDI cables, be aware of slow MIDI interfaces.
MIDI sent to your computer, processed there and going out again may introduce considerable latency, with MIDI cables as well as via USB. In these cases (if latency is a problem for you) consider using another method if technically possible.
Maybe there are some which process and output MIDI and need some time for that, but generally no, soft synths do not create MIDI latency. If softsysths react too late, they may get the notes too late or it's their own slow response or a problem with audio latency, I/O buffer, CPU etc.
MIDI runs separately from audio, the messages contain just numbers and MIDI is relatively slow overall. Timing problems arise in a hardware setup for example when you daisy-chain too many devices or if a MIDI interface is too slow. You can almost be sure to run into MIDI timing issues in a mixed setup with computer, soft synths and hardware modules. Or with timing-sensitive applications like a MIDI guitar when a computer is involved.