Hi, if you have done your research then you probably came across the info that your hamster ideally needs a continious floor space and not various linked hamster cages. For female syria s i highly recommend 100 x 50 cm as a minimium. This also makes it so much easier to keep the cage clean and give your hamster proper amounts of bedding and correct sized wheel, 11 to 12 inches for a syrian. This will all make it so that your hamster exhibits more normal hamster behaviour.
Is your current cage this one shown in this video by any chance as its the only one I know of with an enclosed wheel on the top.
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If it is, maybe watching the video will help you understand why these cages arent suitable.
To answer your question, if it is this cage, yes she has the potential to get sick if the amonia levels build up etc.