Challenge - Class Registration with Breadcrumbs?

I am new member and I must say OpenCart looks awesome! I am considering OpenCart for one of my latest projects. Is OpenCart capable of the following challenge?

OPENCART CHALLENGE:
I would like to use the "unlimited categories" feature of OpenCart to allow users to register for any four (4) types of training classes. The training classes are offered at many different locations, at different dates, and at different time-slots. However, some time slots offer only one (1) type of class. Nevertheless, the combination of location, date and time creates a very large variety of choices. Thus, creating each individual product (training class) is really not efficient because it will take very long time.

BREADCRUMB?
My plan is to create multiple categories which would allow the user to "drill-down" to the class(es) they want to register for. Example of my category setup:

Location 1
-- Date 1
----- Time 1
----- Time 2
----- Time 3
-- Date 2
-- ...
Location 2
Location 3
...

I will create four (4) products (these are my training classes), and then add them to the different categories. Example:

Location 1
-- Date 1
----- Time 1
---------> Class Type 1
---------> Class Type 2
---------> Class Type 3
---------> Class Type 4
----- Time 2
---------> Class Type 4
----- Time 3
---------> Class Type 2
---------> Class Type 3
-- Date 2
Location 2
Location 3

THE REAL/TECHNICAL CHALLENGE?
Now, the important details of the product are nicely displayed by the path/breadcrumb. This is what I need the most! I need a way to record the breadcrumb for every product (training class) that's added to the cart. Otherwise, I would not know for what class (class location, date, time) the user has registered.

How flexible is OpenCart? Is there a way I can accomplish this or should I look elsewhere?

your turning a shopping cart system into a booking system.

Yes Daniel, and it will be awesome if you can tell me if there is a way to record the breadcrumb for every product that's added to the cart?

The bottom line is that I will be selling a product, XYZ, via OpenCart. My products will be in different categories. I would like to know through which category (path/breadcrumb) the product was purchased. Simple in words.

Is OpenCart not capable of such tweak?

I will create four (4) products (these are my training classes), and then add them to the different categories.

In admin panel when you add a product to the categories the category checkboxes list will be huge. Is this ok ?

This sounds more like a set of options for your locations, rather than categories of locations.
By using the categories functions for this, you are simply trying to make your business case fit into a specific technology. You should always look for or code a technology for your business case. Your ideas are worth more than the scripts that run them!!!

Ok, I think I have what you need here http://www.bit.ly/GlobalMegaOptions

You can create global option 'sets' or 'groups of options' and apply them to your products.
Any change you make to your global options will be shown on any product that is linked to that set.
So you can have different options for location one products, location two products etc.
If a specific location does not offer a certain time slot, then you can delete it from the option set and all of your location one products will no longer show that option.

But now you would need to decide whether you really want to use the location as the top level 'product identifier' - as a category; because for me, a location isn't really a product. The class is the product. So I guess you wouldn't even need categories. But that is just talking semantics... I'm not going to tell you how to run your business