I'm not an expert but I believe suckers come from the root stock that the rose is grafted into. So no they are not good for cuttings as they won't come true to the grafted rose.. According to GW last year the good time to take rose cuttings is when ou prune them in late autumn, plunge the cuttings into some well drained compost and they would take.. I did this for the first time last year and the cuttings are putting on leaves and cross fingers will be successful...
Good luck...

I'm with you, Madabout, no good for cuttings at all, I would have thought. Great to hear about your autumn cuttings doing so well. I tried the same thing, and everything was looking good, but the cold got 'em and I lost them again. I shall know better next time.

Both the above comments are correct as commercial roses are budded on to a rootstock which is a form of wild rose. So the sucker cuttings would give you a wild rose, probably very pretty, but not what you want.
As well as hard wood cuttings, you can take green (soft) or semi ripe cuttings around now. Take shoots which have no flowers or remove any flower buds, and dib these into a very gritty compost (I use 50% vermiculite/perlite and 50% compost) around the edge of a largish pot. Stand the pot in water for the first couple of weeks, and stand it in a warm, light place (under the staging in a greenhouse is ideal) but not direct sunlight. You MUST keep it repeatedly misted for this technique to work, which requires dedication, as you must mist at least three or four times a day with a hand mister. Some advice is to place the pot inside a polythene bag, but in my experience, this always leads to the shoots rotting. Rooting will begin in a month or so but don't move the cuttings into proper compost until you see lots of roots protruding from the pot.

Thank you Bertie. I shall give it a go!

Oh didn't realise you could do it now too, really pleased that it seems really easy to do. Free plants is always a bonus

Too right, Madabout!

Thanks for your replies. I remember reading that you should take cutting from this year's growth in September ( I guess those are the hard wood cuttings that you mention Bertiefox. My future FIL gave me six cuttings from his beautiful blue moon climbing rose and he kept saying it was a sucker he took the cuttings from. I wasn't there when he did them so don't know whether it was growing above or below the graft. Out of the 6 one has survived and seems to have a small bud on it ... I guess once that bud opens I will now whether I have a Blue Moon rose or a wild rose!

A guide is that the leaves on suckers usually have an extra pair of leaflets compared with the grafted part.