Yes, you will have no problems. Final Cut Express doesn't actually edit AVCHD, it imports it and converts it to Apple Intermediate Codec, which is a much more editing friendly HD supporting codec.
Your biggest problem will be storage. For doing that type of work AIC takes a lot more space then AVCHD. figure a multiple of 3-7x the file storage size for a single video file, then multiply that by 3 or 4 to account for working space.
So, for example, let's say you have videos to import, the videos total about 6 gig on your camcorder, they will take 18 - 42 gigs of hard drive space just to import the footage.
Figuring 3 to 4x that for editing space, you're gonna need between 54 and 168 gig to edit the video.
Editing HD isn't for the feint of heart, nor for those that don't have plenty of available storage. Also, you'll want to use a drive separate from your internal boot drive of your MacBook, preferably a firewire drive (you can work with a USB drive, if its fast enough and the computer and external drive adapter will work well at usb 2.0 speeds. It's not always the most pleasant situation as you will spend a lot of time letting the system render, and you may have some jitters when initiating playback, but it will work (I know this because I have to edit on my macbook at times with a USB drive connected. I don't use a lot of simultaneous video tracks for many projects, so I usually don't have to worry about multiple simultaneous video streams that would require a rendering every time I changed something. I'm sure that BenB would like to crucify me for saying that, but I know what works and what won't for my setup - don't get me wrong, I'm not recommending using a USB drive for your scratch drive, I prefer to use my hoss Mac at home with multiple internal Sata drive and external firewire 800 drives, but I'm not always at home when I need to edit - I'm just saying you can if you have to, it just won't always be the best of experiences.)