Yes, TECHNICALLY, all your data is collected somewhere and TECHNICALLY Google could know if you were both users.
Your Internal IP/MAC address would be collected by McD however as I doubt they give you a public IP. Google knows the public IP and your account. The other McD MIGHT or MIGHT NOT be connected over the same VPN to a McD concentrator (in order to be more efficient at logging your information, collecting it for advertisements and legal reasons) that uses a common ISP so you MIGHT have the same public IP address. It doesn't really matter actually, all Google sees is a connection from McD. McD however might have control over the DNS etc. and could intercept all traffic so they MIGHT be able to see your laptop and correlate it with security camera's etc. (that's if you go into forensic IT)
To do it correctly (you're trying to be anonymous) you may (in order of what's better)
a) Use SSL for all traffic so McD can't intercept your sessions with Google.
b) Use TOR or another system to tunnel your traffic all over the Internet
c) Use private VPN's through a few hacked hosts in several countries with logging turned off to tunnel your traffic.
d) Don't be at a public place with security camera's
a) Will protect you when interfering with most non-malicious organizations (your grocery store, the bakery on the corner)
b) Will protect you when interfering with medium-to-large corporations (McDonalds, Watchtower)
c) Will protect you when interfering with public government (FBI, IRS) and larger US-based corporations (Microsoft, Google)
d) Will protect you when interfering with private government (NSA, CIA) and the largest multinational corporations (Bayer, Monsanto)
Nothing will protect you when you're interfering with enough money to put a dent into the economy or messing in government wars (like Wikileaks-level).
The best thing to do is wardrive with a stolen and cleaned laptop, change your MAC address (it's possible and simple to do in software - Linux OS just allows you to type a new one in) and use several open WiFi points you hack with custom firmware so it doesn't log anything from your car or van (best stolen just in case). Then burn all of the possible evidence, your clothes, your disguises and then take the laptop's hard drive out in order to destroy with self-made (not bought) thermite. Also, don't use credit cards or do anything else that you would habitually do on the Internet, it can all be traced back technically and with enough power into each of the corporations that tracks you for advertisement purposes. Stay away from camera's and don't look up, wear a cap and sunglasses (so satellites and drones can't identify you), use several counterintelligence techniques to lose tails and be away from all RF transmitters before destroying evidence, use GPS and cell phone jammers, walk through the woods for several miles before getting back to your own home and MAYBE they won't find you.