That depends on how large is large and which image size you use.
My collection of about 4000 Discs with Cover Image Size of 500x700px (for both front and back, you can choose to only sync the front cover) takes up about 1,13GB.

Hi Cubby,
Same phone.  I had the same questions.  I was was just getting more confused by trying to anticipate problems that might arise.  I spent my $3 for the App and followed some instructions for getting things going and the only problem I recall was having to type in a number rather than a name to get the phone to talk to the desktop computer.  Everything went so easy I don't even recall where I found the instructions I followed.  I have 5328 discs and the only problem I noticed was on some screens there is some text that has the very bottom missing; perfectly readable though.  Everything else looks and works so great that I hated to mention this but didn't want you to think the problem was unique to you.
My suggestion is to just go for it and address any problems that may arise when they do.
Jim F.

There are two ways for transferring the data. If you have Wi-Fi at home you can transfer the data from your dektop computer to your phone (and the other way around) via your router. If you don't, then you have to pull the data from your online collection. While using the app it doesn't eat up your mobile data, as long as you don't access the online database. The app itself can not be moved to the SD card but the database can be stored on it.

Hey cubby,
I believe I have the same Tracfone as you.  I don't know what you're current setup is but regarding WiFi I believe that if your current setup has the ability to talk to a router only a wireless router is needed.  No modem or internet access needed.  I thought of you when I was in a thrift store several days ago and saw two wireless routers both of which were less than $5.
As far as eating up data that isn't an issue as has been stated.
The Profiler app has been great and have yet to find any deficiencies that the beta version is being designed to address.  It just seems to do everything that's of interest to me.  The only problem I noticed was the inability to read barcodes when adding a disc. But I believe the problem is with the phone as I've not been able to read any other barcodes.  It does read those "QR" codes frightenly fast however.
Jim F.

For downloading your online database I'd recommend to use some public Wi-Fi. I don't know about the situation in your area, but in my city there a many free Wi-Fis in cafés and shopping malls. But I have no idea how long that would take with such a large collection.

I sync via WIFI with my Desktop Profiler which is faster than syncing with the online Database, and the initial sync takes long enough that i start it, let it sit and go away. So i am guessing that for 3600 from the online database you're looking at an hour at least. But then again this is just a very vague guesstimate.

I think the problem is that he doesn't have wireless LAN at home...

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Thanks rdodolak, that's what I was looking for.

But as I said, this is my first Smartphone, so all of this is a little over my head. Probably will need help, step by step.