There's really no reason why not, as long as you have the funds available to pay for it there & then. Depending on the bank and/or branch you use, this might mean having the actual cash to pay for it or else be in a position to have the amount debited to your account immediately. Naturally, it would not be given to you instantly if time was required to clear a cheque or something.
Might not be a bad idea to give your branch a buzz to let them know you want to purchase a draft. I hold my account in one branch of a major bank and do whatever day to day banking that needs to be done in branch other than the account holding branch. It does sound nuts but if I am making a large withdrawal, my local branch needs the ok from my account holding branch. Might just be worth that phone call to avoid hassle when you go to get it.
Thses fees are crazy.
I recently got a large draft from Ulster Bank and it only cost mer €2.25 and yes they do have to contact your local Branch. You get the Draft there and Then. It can take up to 15 minutes to get everything sorted.
They also give you the draft in an envelope which is a nice touch.