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I am fairly new to studying communication systems.
When it comes to different digital modulation techniques, does the effect of an additive complex noise (a) introduced by the system, and (b) by the channel vary depending on the type of modulation used?
Moreover, is the noise introduced by the non-ideal system can be treated exactly the same as with the noise introduced by the channel (that is, the approach to work around and solve them are the same)?
This is up to how you model noise and channel.
In the classical, most-commonly-used models, the channel is actually noise-free and the noise is only added at the receiver.
If you have a different channel, that's kind of specific to how your special problem is being modeled, and we don't know that.
But since you say, you're new to communications systems: The cases you're most likely to encounter are actually that the noise only happens at the receiver.
If that's not the case, look for the context in which you're working. For example, if you're in the context of diversity combining, and are considering a channel that has interferers, e.g. because you're trying to implement optimum combining, then your overall noise is usually described by a covariance matrix – in which you don't really care about where the noise energy actually comes from (there's the assumption that receiver noise is uncorrelated and hence manifests as diagonal entries in the matrix).
