As Geoff has said Ezy, the non-motorized axis is for dec adjustments. How much adjustment you need to do will depend on how well your mount is polar aligned. Theoretically if your mount was perfectly polar aligned you wouldn't need to touch it. Unfortunately, due to mount limitations and tolerances and your ability to polar align, that is usually not possible. Even the best telescopes in the world need some adjustment in Declination at some time in their tracking.
Having said all that, if you are manually guiding for photography (which you would be doing as the standard motor drives for your mount don't come "naturally" capable of autoguiding) you can use the manual dec adjustment knob for minor adjustments. It will take some practice though, and your success will be very much dependant on the quality and stability of your mount. Having a dec motor though would make life easier as then you remove the need to touch the mount at all therefore removing one source of potential vibration/movement for the mount.
If you are thinking of getting into astrophotography one of the three things that you cannot really skimp on is the mount. Without a good STABLE mount with regular gear movement (periodic error) you may find it extremely frustrating for anything more than piggyback photography.
That doesn't mean you can't do prime focus and other types of DSO imaging (I'm ignoring planetary here as you should have np with any type of motorized eq3 mount and above), it's just that using the mount you have or even an EQ5 you may have to do quite a bit of initial and ongoing "maintenance" and "tweaking" to bring it up to scratch.
"To be forewarned is to be forearmed" ie. More research so you know the capabilities and limitations of different mounts you can afford.
And we haven't even touched on OTA's yet
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