When I bought a Trek FX 7.3 instead of the 7.2, the bike dealer told me that the tires were the same. They looked narrower, but I thought it was just that I was used to my other bike. I found out later that the FX 7.3 indeed has narrower 32 mm tires. Can I put 35 mm tires on my FX 7.3?
32mm to 35mm is a small change. It's not going to make a huge difference in ride quality and because it's a small change, any bike that comes with 32mm tires is very likely to handle 35mm tires with no difficulties.
The 7.2FX and 7.3FX are the same frame, but a different fork. It's hard to be sure from the online description, but probably also the same brakes. The wheels are different, but it's a small enough tire size change that it's not a problem. All the geometric specs are identical for all sizes between the two models.
If the 7.2 works with a 35mm tire, the 7.3 will almost definitely work with the same 35mm tire on the rear, and very likely work with the same 35mm tire on the front.
A 35mm wide tire should be 1.5mm wider on each side than a 32mm tire, and will have a similar increased outer radius. 1.5mm is the thickness of a US penny (or a smidge more than the thickness of a dime), so you can use a couple dimes to measure.
Is there at least 2mm of room on each side (and top) of the tire where it passes through the top of the fork? Same amount of room or more where it passes through the brakes? That's the most likely problem areas here.
Double-check the back if you're still worried: is there 2mm clearance around all sides of the tire where it goes through the brake, where it goes between the seatstays, where it goes through the chain stays and where it gets closest to the seat tube?
If all those check out, then you're in the clear. If it's a close call, you'll just have to try it, or go into the shop and ask them to help you see if it'll work.
Honestly, I wouldn't risk it. It's always best to go with a replacement that you know will work and especially with tires! So really it's up to you but a close call for sure with the size dimensions you've explained here.
The difference between 32 mm and 35 mm tires will only really be seen if you're using exactly the same tire in a slightly larger format. You may notice over time that if you switch manufacturers their profiles may change slightly and this may affect the effective clearance you have at your stays.
Having checked over the 7.2 frame it appears that there will be plenty of additionally available clearance to allow for a wider tire.
Best thing to do is buy from a retailer who will be happy for you to return the new tires if there is an issue.