You haven't said which variety of clematis; if its a species such as montana, it'll be too big for your trellis. Otherwise, the vast majority of the clematis hybrids climb by means of modified leaves called petioles, and these need something thin to wrap around, something like mesh or a thin pea stick. Unfortunately, your trellis isn't something they can attach to because of the thickness of the struts. That's problem one; second problem is, if you don't place the obelisk over the plant so that its in the middle, but leave it to one side as you describe, if the clematis could attach itself, it would only climb up the one side it can reach. The thickness of the lathes also means reduced light for any plant trying to grow up through the middle of this structure.
The best type of obelisk for clematis is actually metal, because it usually has much thinner struts and is more open - the one you have is better for growing a twining plant, such as honeysuckle, which will easily wrap itself round the supports and won't be too troubled by being in the middle of the obelisk - the obelisk should be placed so that the plant is in the centre.
If you really want to grow clematis up it, you could cover it in chicken wire or actual clematis mesh, which clematis can use as a support, but this means you will not see so much of the obelisk itself. Otherwise you'd need to tie on growths yourself all the time, and that's not easy with clematis, the stems are quite fragile.