VFA is not a thick paper. It is only 260 g/mē.
Weight has little to do with thickness.
Epson Velvet Fine Art Paper is 0.48mm
The sheet feeder takes paper 0.003 to 0.004 inch (0.08 to 0.11 mm)
It may go through but will probably damage the sheet feeder for gripping thinner paper being 4x over the maximum thickness.
That is a lot thinner than the 3880 which allows 0.27mm. So looks like the design has changed on the sheet feeder from the 3880.
From the somewhat vague manual ....
"Use the front manual feed tray and the rear paper support to load fine art media.
Note: You can load fine art media with a thickness of 0.012 to 0.028 inch (0.3 to 0.7 mm)."
Poster board: 0.047 inch (1.2 mm) to 0.059 inch (1.5 mm). That would be the flat path.