No. A chair, yes. (Also other words for seating) Draw up something else would normally mean sketch or draft rather than move.

'Draw up' in the sense of 'bring closer' tends only to be used with chairs. It's also quite dated as an expression, and I agree with @Jewel that 'pull up a chair' is more common nowadays. I wouldn't worry about the usage 'draw up' in this sense, to be honest: it is not especially useful. For other objects, such as the photo in your example, you'd say something more straightforward e.g. 'Bring the photo a bit closer'. By the way, when I saw your title, the first meaning of 'draw up' that came into my mind was 'draw up a contract' or 'draw up some plans' (as in 'prepare'). This is probably the commonest use of the transitive 'draw up' in modern English.

Let’s have the lawyers draw up a contract based on what we discussed. (Good) Let’s have the lawyers draw a contract up based on what we discussed. (Less good) He held up the photo... He brought up the photo ... It depends on what he was doing exactly and why he could see it better. But not “draw up.”

For moving something, "pull up" is more natural/colloquial. "Pull up a chair, please." "He pulled up the photo to show us." "It's raining - can you pull up the car?"