It definitely has a tangible effect. For example the National Rail going east of Liverpool Street runs equidistant to the Central (to zone 4) and District lines, and has more 'person under train' incidents. Whenever such an incident occurs, both those tube lines plus the National Rail line which runs alongside the District are swamped.
The flip side is that it's not enough to prevent suicides on your line - you'll still get unusual peak capacity issues if it happens on a neighbouring line - but at least you can keep your own trains running.
The flip side is that it's not enough to prevent suicides on your line - you'll still get unusual peak capacity issues if it happens on a neighbouring line - but at least you can keep your own trains running.