No, yEd cannot automatically re-label your nodes with consecutive numbers.
Using a VisualBasic script, you should be able to achieve the desired result with the following approach:
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Select all nodes using CTRL+A. (If you have multiple labels per node, select all node labels instead using "Tools" -> "Select Elements".)
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Enter a place holder text (e.g. [LABEL]) in the "Text" field of the properties view in yEd's lower right corner.
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Save your diagram as GraphML. (GraphML is an XML-based format and is well-suited to post-processing.)
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Use your script to replace all [LABEL] occurrences in the GraphML file with consecutive numbers.
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Open your modified file in yEd once again.
Note, if there are group nodes in diagram, you need to open all closed groups for this approach to work.