Can I use regex in a DCR custom text logfile filepath?

You may try :

1. * (asterisk): Matches zero or more characters in a single directory level.
2. ** (double asterisk): Matches zero or more characters across multiple directory levels.

"filePath": "/var/log/**/*.log"

{
  "dataSources": {
    "extensions": [
      {
        "name": "TextLogs",
        "streams": [
          "Microsoft-TextLogs"
        ],
        "extensionName": "TextLogs",
        "settings": {
          "filePatterns": [
            {
              "filePath": "c:\\appserver\\logs\\*\\server\\*.log",
              "format": "json"
            },
            {
              "filePath": "c:\\appportal\\logs\\*\\portal\\*.log",
              "format": "json"
            }
          ]
        }
      }
    ]
  },
  "destinations": {
    "logAnalytics": [
      {
        "workspaceResourceId": "/subscriptions/{subscription-id}/resourceGroups/{resource-group}/providers/Microsoft.OperationalInsights/workspaces/{workspace-name}"
      }
    ]
  }
}