Does Raising the Nasal Bridge Have Essentially the Same Effect As Epicanthoplasty?

The amount of nasal bridge augmentation in that area will not affect the medical epicanthus. Raising the bridge of the nose CAN make the eyes look closer together, so in some cases you may need to under-augment the bridge to prevent this. 

You'll need a separate epicanthoplasty procedure to remove the canthal tissue.

I don't think that raising the nasal bridge will have a huge impact on your epicanthal folds and they would not be considered equivalent in fixing any canthal issues. My recommendation is always to be conservative in my approach, to never burn any bridges, and try to create the most natrural results... Armed with that philosophy, I would recommend just like you suggested and tackle the blepharoplasty first and hold off on the medial canthoplasty until the nasal implant is in place. My thinking is that it is easier to reverse th nasal bridge work than the medial epicanthal fold. And by staging it, you minimize the possibility that you would need to revise the medical canthus at all. good luck, hope things go well

By placing an implant, or an injectable filler, to raise your nasal bridge, the illusion of wider eyes may be seen temporarily.  However, the structure governing the actual width of the eye will eventually bring the eye openings back as the skin over the bridge relaxes.  This usually takes 3 to 6 weeks to experience.  If you have strong epicanthal folds, I suggest you consider the surgical epicanthal release for a long term result.