That sounds great - I have heard it is a great course! I am using the
Al-Kitaab series in my own time (outside of Uni which has another syllabus), from Georgetown University Press and am thoroughly enjoying them so far. Some Egyptian is introduced along with the formal/standard in order to help begin seeing similarities and differences.
The only problem I can see with what you are doing is that the difference between spoken (Egyptian/Syrian/whatever) and the written/formal Arabic (Modern Standard Arabic) which is most likely what you will find in the grammar books can some times be due to the grammar itself and/or the accent and pronunciation of certain letters.
For example, in the Levant, they do not pronounce
ق as "q", instead they pronounce it like
ء the hamza. thus
قهوة "qahwa" (coffee) becomes "'ahwa" although is written the same.
ليلة القدر "laylat al-qadr" becomes "laylat al-'adr", for example.
إذا "idha" (if) becomes "iza" because
ذ is pronounced like
ز. The reason is due to making things easier and quicker to pronounce - it is hard to go from "qaa" to "dr" in qadr, and from "dh" with the tongue at the front of the mouth to "aa" in idha, for example.
In grammar also the dual tense (for only two things/people) is rarely used - the plural is used instead although we find the dual in the Qur'an and even modern literature. Also things like the endings for plurals ين/ون does not always show although it is important in Classical Arabic.
You know how it is - in English we have the same - in order to get the message and point across we don't all speak "Queen's English" all the time. I am from Scotland so have my own accent, but I live in Australia which has its own accent and slang way of saying things, the same as America and so on. Not to mention how we write and structure things is also different to how we speak.
This is just something to bear in mind when you are listening, because if you already know how to pronounce the Arabic alphabet (e.g. from learning how to read Qur'an when young) then you might wonder why some things don't "sound" like they are written. But if you are just picking up the speaking then go for it - listen and repeat as much as possible! It is still all Arabic and all helpful to learn - don't worry about it but just be aware - I hope this hasn't confused you more than it has helped...
Good luck! Arabic is a beautiful language.
dawood