Are imine or amine bonds similar to ethereal bonds, from the perspective of an enzyme?
This does depend a lot on what the enzyme does and what it expects. Take the following three structures, one from an ether (e.g. diethyl ether), one from an amine (diethyl amine) and one from an imine (N-ethylethanimine).


Scheme 1: Ether linkage, amine linkage and imine linkage (from left to right) including hydrogen atoms on adjacent carbons.

When looking for a ether, an enzyme may well attempt to form a hydrogen bond to the ethereal oxygen. This might work in the case of an amine — there is a spare lone pair on nitrogen that can accept hydrogen bonds, but the additional hydrogen present can present ordering and space problems —, but would in the case of an imide.

However, note that the carbons next to ether and amine bonds have four atoms attached to them (two hydrogens and another carbon each), while the imine has only one hydrogen. The $\ce{C=N}$ bond is planar, meaning that the configuration of the neighbouring atoms is also relatively fixed. Thus, the imine may have a pretty different shape — and may not fit into the enzyme’s active pocket. This might actually also mean that the imine cannot accept the hydrogen bond offered by the enzyme because it cannot orient itself favourably.

As I said above, it depends on the enzyme whether it cares about hydrogen bonding more or whether the overall shape is more important. In general, I would consider an amine to be closer to an ether structurally, and therefore more likely to be accepted. Possibly, the amine hydrogen can point away, allowing for the amine to accept a hydrogen bond nonetheless. In that case, the amine would be the clear winner.

All these heteroatom bonds are clearly different from $\ce{C-C}$ bonds due to the bonds’ inherent polarity (electronegativity of $\ce{O}$ and $\ce{N}$).