Probably not a good idea with the foam, or any infill. In my experience, when we dont give water a place to go, bad things happen. Remember that any water will find it's way to the interior of the brick, and flow down the backside to drain. If this is not possible, and the water remains in the brick, it could cause a catastrophic failure if it ever freezes.
Beside that, it was developed in Europe, and these are some of the quotes I found for a wet area.
Cavity masonry walls were introduced on the exposed western coasts of Britain and Ireland in the nineteenth century, to stop wind-driven rain from penetrating to the inside surfaces. They gradually spread to other, dryer, parts of the country, because the air layer trapped in the cavity was found to provide a degree of thermal insulation. Since 1945 this insulation quality has been enhanced by using lightweight blocks, rather than bricks, to build the inner leaf of the wall. But the main reason for building cavity walls has always been to keep the rain out.
Since the 1980s, the Building Regulations have required new houses to be built with insulation material in the cavity. As long as they are built properly, this insulation should not compromise the walls resistance to rain penetration.
In most cases, the insulation is fixed to the inner leaf, leaving a narrow cavity to intercept any rainwater that penetrates the outer brick leaf. This insulation material is usually in the form of rigid foam boards, which are intrinsically waterproof, or semi-rigid mineral-wool or glassfibre batts, where the fibres are aligned vertically so that any penetrating rainwater should drain downwards in the cavity and not have the chance to penetrate across to the inner leaf. This is important, because the Building Research Establishment has found that single-leaf brick walls ALWAYS leak when exposed to wind-driven rain. The leakage occurs at the vertical (or perp) joints between adjacent bricks, because of drying shrinkage in the mortar. It is not a question of poor workmanship; it is an inevitable property of this form of construction.
Many readers with single-leaf brick garages attached to their cavity-walled homes, for example, complain that rainwater penetrates through from the outside when they are subjected to wind-driven rain, resulting in puddles on the garage floor. Well, if the rainwater is penetrating their garage walls, then the same thing will be happening to the brick outer leaves of their living rooms and bedrooms, but as long as the cavities are left clear, the water should run down the inside of the brickwork to foundation level and never be noticed. Until the recent fad for cavity wall insulation took hold, the only times rainwater penetration was a problem was when the steel wall ties were dirty with mortar droppings and/or built sloping downwards from outer leaf to inner leaf, or the cavity itself was blocked at low level with mortar droppings or other debris. In those cases penetrating rainwater could track across the cavity and show up as damp patches on internal decorative surfaces, but the solution was relatively simple cut out a few bricks and clear the rubbish out of the cavity, or replace the offending wall ties.
Dampness problems caused by cavity wall insulation do not generally occur in houses where the insulation was built-in from new. They happen in houses which were built prior to the 1980s, with clear cavities, which have subsequently been filled (referred to in the industry as retro fill). The material which has attracted most complaints is blown mineral-wool fibre. This material consists of loose fibres which as the name suggests are blown in through holes drilled in the brick outer leaf. The manufacturers and installers claim that the material is water-repellant, and that it cannot allow rainwater to penetrate across the cavity. However, my own researches show that far from being waterproof it can soak up water like blotting paper. Samples sent to me by readers have been found to hold a startling 243 per cent moisture ie nearly two and a half times their own weight in water.
I have received dozens of letters and e-mails from readers who say that, following installation of blown mineral-wool fibre, their inside walls have become damp and mouldy, and their homes have become uninhabitable and unsellable. And in every case the installers and their guarantee provider CIGA (the Cavity Insulation Guarantee Agency) has refused to acknowledge that the cavity wall insulation was the cause of their problems. In every case the installers and CIGA have insisted that the dampness problems were due to construction faults in the building (even though these are supposed to be identified by the surveyor prior to installation) or to lifestyle condensation caused by the occupants (even though condensation had not been a problem prior to the CWI).