Yes, you can! And that is the way many gardeners go about it. Often, manual removal of weeds is in fact the most thorough way of removing them.

Being a 'landscaper' and being 'knowledgeable' do not always go hand in hand :-) Spraying a herbicide is the quick and dirty way of doing things and many so-called landscapers prefer that option over a more benign and comprehensive but more time-consuming and labor-intensive approach :-)

Go ahead and get as many weeds out as possible, with roots, and look for any remaining roots from the sod. If left, those can present an ongoing issue. Then amend your soil as desired and plant. A nice thick mulch covering after planting will definitely help to keep weeds to a minimum as well as protect the soil and help to retain moisture. It won't prevent ALL weeds from returning but neither will spraying with RoundUp!!

ps. you are NOT crazy and it was uncalled for for him to say so :-)

I personally would probably have used Roundup due to ease and it would help keep the weeds down somewhat. But I have also dug up sod and turned it over and pulled up or hoed the weeds. If the sod is bermuda grass I would have definitely used roundup. You will never get all of the runners and it spreads very fast.

Your landscaper neighbor thought it was crazy how you were doing the job due to increased labor. You will think he is crazy for using all those chemicals. I tend to fall in the middle. If you have the time why not dig out the weeds. You will get a good workout and not have to pay for a gym membership.