Based on the science we understand today: no.
I agree with MichaelRichardson that planet-based power generation would be difficult to believe under normal circumstances. But what if circumstances weren't normal? What if your civilization's tech was better than ours?
let's bring a retrograde orbit into play
...Retrograde planets do exist – two examples are the exoplanets Kepler-2b and WASP-17b. The process responsible may be what’s known as the ‘Kozai mechanism’, in which the gravitational effect of a distant third body can cause a perturbation in a planet’s orbit that slowly moves the planet into a tilted and elongated orbit. This tilt eventually becomes so extreme that the orbit is flipped over. (Source)
The article continues with a very brief discussion of how non-tilted/elongated orbits (both of which would reduce power generation) can be avoided, but with more likely somewhat unusable outcomes. Let's ignore all that! We have evidence that planets can exist with retrograde orbits. Your planet has a perfectly circular retrograde orbit that's flat in relation to the star's equator! Who's to say it can't be done? The universe is still surprising us. So...
The value of the retrograde orbit is that it enhances the velocity of the magnetic flux in relation to the power generating coils. Think of it this way: the alternator in your car is fixed to the chassis of the car. This means that the velocity of the stator (the magnetic coils fixed to the chassis) is zero. The only motion is the velocity of the rotor (the coils turned by the drive belt).
In "normal circumstances" the planet is orbiting in the same direction as the rotation of the star. This is like the stator of your alternator turning in the same direction as the rotor. This reduces the difference in velocity between rotor and stator and reduces the amount of generated electricity.
But when the planet has a retrograde orbit, it's a situation that's philisophically better than a fixed, non-moving stator. Now the proverbial alternator stator is moving contrary to the rotation of the rotor, generating more electricity.
And let's handle the reality that you'd need big coils
OK, so we've put a check mark in the believable column. Now let's deal with a question mark in the unbelievable category. Your neutron star certainly has a big mother-hubbard magentic field — but it's not that big. It can't be that big. Your planet (one assumes) is in the star's goldilocks zone and magnetic field strength is subject to the inverse-square law (and possibly the inverse-cube law). Long story short, the stator in your car's altenator may have more power-geneating ability than the neutron star. But, as science-based as we want to be, the goal (at least my goal) is suspension of disbelief.
This means you have big honking coils on your planet. Big honking coils. Quartersphere (think hemisphere then cut it in half) spanning coils. They're impressive and hard to defend against terrorist attacks...
... but they're big enough to rationalize power generation from a neutron star — at least if they bisect the planet's equator.
It's worth noting the planet's rotation direction is irrelevant becuase, regardless the spin direction, the coils are moving maximally against the motion of the neutron star's magnetic flux half of the time, and minimally the other half of the time. Changing the spin direction simply reverses which half is which.
Of course, you could tidally-lock the planet with an axis of rotation that's perpendicular to the star's equator so the coils are engaged without the hassle of having do deal with the sinusoidal output due to planet rotation. Yeah, that's the ticket!
