720p is only 1280x720 so yeah it should play it at that (not sure but I guess it would play at 1080p but just downscaled). But just make sure the processor of the laptop is fast enough for 1080p content (or alternatively if the graphics card can process the video).
But then there is HDCP (High-bandwidth Digital Content Protection). Blu-Ray discs simply won't play unless all the pieces in the chain support HDCP. If the laptop is old it might not work, if it has HDMI output it probably does work, and.. yeah... I think the graphics card and monitor need to be HDCP compliant. I don't know how exactly this stuff works on laptops.
And then you also need a software like WinDVD or PowerDVD HD.
OR, you can use something like AnyDVD HD (which costs) to bypass all those protections including region coding (and so you can use any software you want that can play HD video).
I remember when I got my Blu-Ray drive back in 2008 and I had HDCP compliant graphics card and monitor but it didn't help because I also needed to send the signal from computer to monitor with HDMI cable (which if I remember correctly my graphics card didn't even support?!?!). So in order to view my original discs I had to bypass the protections... which is illegal here now.