I doubt you'll be able to fit 38mm tires on an older road frame, it all depends on your chainstay width. Measure the width of the chainstays with the existing 27" wheels at the point where the wheels passes by the chainstays. You'll need at least 3mm per side, 38mm tires will be closer to 35mm on road rims with a 25mm outside dimension (like Mavic a319 etc).
I have given up on 38mm tires on an older frame, even when I mash the stays to fit wider tires, the tire is too tall and I need to let the air out of the tire to install the wheel in the dropouts. Now I run 35mm tires, no need the "clearence" the frame, still have to let some air out of the tire to install the wheel in the frame.