Can ROS work with a Intel® Xeon Prozessor E5620 ?
that's a standard amd64
compatible x86
CPU with 4 cores, so the answer would be: yes.
See REP-3: Target Platforms for ROS 1 supported CPU architectures, and REP-2000: ROS 2 Releases and Target Platforms for ROS 2 supported CPU architectures.
What made you post this question? Did you read anything which made you ask it?
Note btw: as always with these kind of questions: we can only answer whether the code/binaries are compatible with the CPU architecture. Whether the performance of the specific CPU you mention would be sufficient for your use-cases we cannot say, as only you know those use-cases.