Hi,
For sure it has influence:
Since you are not very specific ... let's just talk about signal outputs (source)and signal inputs (load)
Each device datasheet specifies the signal output and input characteristics.
Some devices are designed to have very strong, regulated outputs. Like an OPAMP.
The output impedance usually is below 1Ohm, thus connecting a load of several kOhms won't change the output much
But there are devices with more weak outputs, maybe in the kOhm range, then connecting a low ohmic load will cause to drop the output significantly.
But even if an Opamp output is strong, there still are limits. Like maximum current you may draw.
Let's say 10mA. If you try to draw obove this limit, not only the output will drop, but the internal regulation loop will saturate, and it takes rather long time to recover from this state.
So there will/may be voltage drop, extended timing, overheat, instability .... and so on.
We professionals rely on the datasheet informations and mathematics.
Klaus