Is it possible to create a Marketo landing page that will pop up as an overlay from our website?
Melissa, this is certainly possible, as most modal (a.k.a. overlay, popup, lightbox) JS libraries will allow you to place a Marketo LP in an IFRAME.
However, you should think twice before doing this. IFRAMEs create a set of small but significant complications: referrer tracking, UTM params, Munchkin, Thank You URLs, and RTP are all affected. Every one of these can be solved with some relatively lightweight JavaScript, but you should be ready for side effects. Be in contact with your developer and test all angles before embarking on this.