I am a surveyor, albeit on commercial properties. To answer the original question, yes about a week but don't forget it needs to pass through your lender first. To pick up on another point, he/she would not probably answer questions over the 'phone. Their client is the lender, not the borrower, so there is no direct relationship with the surveyor and buyer. They also get paid only a fraction of what you will have paid the lender for the mortgage valuation, so it would not be cost effective for them anyway.
Always sensible to pay the bit extra and go for a Hom******s Report. If that flags defects needing further investigation, then escalate to full structural or get in specialist timber guys, structural engineers, or whatever might be required. Anything serious found will either put you off buying and therefore save you making a bad decision, or almost certainly open the door to reducing the purchase price (with the reduction no doubt being well above the cost of the survey).