Yes. BricsCAD supports connecting to Web Map Service (WMS) endpoints using the MAPCONNECT command, which lets you add map imagery from many public and government-hosted WMS servers into your drawing.
Before adding WMS data, Bricsys notes you must set the drawing’s geographic location using GEOGRAPHICLOCATION.
See: MAPCONNECT command (WMS connections).

BricsCAD also supports displaying online maps inside a drawing using GEOMAP, and the related GEOMAPKEY workflow for assigning an API key.
Bricsys documentation specifically references Esri Maps Keys for access to Esri online maps.
See: GEOMAP command
and GEOMAPKEY command (Esri Maps Key).

For importing vector GIS data as CAD entities with attributes, BricsCAD provides GISIMPORT, which Bricsys documents as supporting SHP, GML, KML/KMZ, and Esri Geodatabase formats.
See: GISIMPORT command
and GIS Import dialog box.

Related references

• BricsCAD MAPCONNECT (WMS setup):
  Bricsys Help Center
• GEOMAP and GEOMAPKEY (online maps and API keys):
  GEOMAP,
  GEOMAPKEY
• GISIMPORT (SHP, GML, KML/KMZ, Geodatabase import):
  GISIMPORT
• Example third-party WMS guidance for BricsCAD Pro (Nearmap):
  Nearmap BricsCAD Pro WMS Integration