You have to understand that MIDI is just like playing a keyboard, it doesn't do anything for audio - so the audio effects largely depend on the instrument you are playing.
For instance, if you have a synth in mono-legato mode with some portamento, it may well glide when you play overlapped notes. If portamento is turned off and it's in polyphonic mode, it won't.
So, set up your patch to be mono-legato mode and a bit of portamento, and then overlap your notes.
Some synths handle this differently, so without any further info, you'll have you look in their manual as to whether or how they do legato playing.