It is possible to infuse with Easycell foam sheet but you'd need to make small holes at around 50mm centres in the sheet thicknesses below 10mm in order to do it in one go. This, however, will leave you with dark spots on the cosmetic surface where the holes are in the foam as witness to the excess resin in these areas.
I've not used the 10mm pre-grooved sheets, but I'm guessing that this might also leave some evidence of the grooves on the cosmetic side once infused?

The safest bet would be to infuse your top and bottom panels first, then bond your foam sheet between them afterwards using laminating resin in order to create your 'sandwich' panel.

Be wary of weighting things down too heavily or using vacuum to help create the secondary bonds, though, as the slightest trace of any cured resin particles, for example, that might be sitting between your panel and the surface on which your doing the bonding will likely create dimples in the panels' surface. Don't ask how I know this! :-)