Answering the OP's question - no, mixing them does not negate the benefits.
There seems to be a lot of misunderstanding of how balanced topology is used to reject noise. A fully balanced system will sum the positive and negative signals at a number of points in the chain, to cancel noise that has crept into those two feeds, so that you get a clean single-ended signal, and then it is split again (or transformer-buffered) for the next stage. Each balanced stage achieves benefits that are independent of prior or following stages. There is no need for a system to be balanced end to end in order to get the benefits of balanced operation in one stage.
The downside is that a balanced system will therefore tend to have more active or transformer buffer stages inserted into the signal path, and this is not usually a good idea in gear made to a low to mid-price.
Single-ended cables have greater interaction with the system's ground plane, than do balanced cables, and this is more likely to account for sound character differences in typically short audio cables, than is external noise rejection (RFI, EMI...).
Additionally, the design of many single-ended interconnects does not translate into a balanced design without significantly changing the simple electrical parameters of LCR.
The trouble is that it costs more to build balanced gear than single ended gear, so it is not obvious whether, dollar-for-dollar, one is superior to the other. And a lot of XLR inputs are often not balanced at all.
As a wild generalisation - where gear is designed for single-ended sound and balanced interfaces are added as an after-thought, single-ended will usually sound better. The reverse is also true. Gear designed around balanced operation will usually sound better with balanced cables.
