Would this result in lots of dropped packages at 100Mbps link due to the full buffer-memory at the switch?
Yes. Note that not only packets carrying your UDP flow are dropped but any packets crossing the bottleneck may get lost.
If the Client uses TCP-traffic, all is fine due to the redundancy in the TCP-protocol?
I wouldn't call TCP redundant but it provides reliable delivery and - more importantly here - congestion control. TCP detects in-path bandwidth capabilities and problems, and throttles its traffic accordingly. That way, drops across the bottleneck may remain low, not only for the TCP stream in question but also for any other traffic.
Essentially, any application using UDP with significant bandwidths must implement its own congestion control.
If that bottleneck in your network is by design then it's a grave architectural problem.
Another significant problem in that network is the long chain of switches. Generally, you should create a tree of switches, not a chain: a 'core' switch in the center/root, and as many 'access' switches around it providing end-node connectivity as required.
If you can't get enough ports that way, you add an intermediate 'distribution' layer. A tree topology reduces the network diameter, the susceptibility for bottlenecks and it minimizes impact from link failure/degradation.