How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band?

If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the discrete wavelet packet transform (with Daubechies wavelet) for denoising purposes.

My frequency content now is 0-937kHz in level 0 and divided to the power of 2 with respect to the level (as in the binary tree).

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I have two questions:

1. If my 50 Hz noise is high in amplitude comparison to my signal of interest, looking at node of "43.94Hz-59.59Hz" frequency band at level 6, If I perform thresholdolding the noise would still be present in the signal as it would have high amplitude, correct? While to remove it completely I would need to zero out all coefficients in that band.
2. If my 50Hz is smaller in amplitude than my signal of interest, performing thresholding could theoretically remove the noise while keeping my signal of interest, correct? (theoretically because it depends on the threshold level and method)

Please correct me if I am wrong along the process. I am still trying to understand the benefits and drawbacks of wavelets.