More info on the tank type would help as would more info about the stand top.
Is it a rimless tank or a braced/rimmed tank?
What size tank?
If rimless, will you be putting 1/2" foam or 1" foam between it and the stand top?
What type of material is the stand top and what kind of material is it --- MDF, plywood, wood plank (i.e. dimensional lumber), metal?
How thick is the material?
When you say deflection, are you actually seeing the top deflect when you put pressure on it before the tank is even resting on it?
As for long term effects...
Within a few weeks to a couple of years, significant deflection will allow the bottom and/or front and back panels of a glass tank to sag under the weight of the water and rock. That will put excessive and uneven pressure on the silicon joints causing one of them to eventually fail.
Deflection in the top can cause this, as can a top that is uneven (e.g. not perfectly flat).
Putting foam beneath a the tank compensates for slight deflection and unevenness. It essentially conforms to the 'voids' and helps to more even distribute the weight of the tank across them.
I'm no pro, but the maker (solid reputation) of the new 65g I am setting up informed me 1/2" foam should be adequate to compensate for any unevenness or slight dips of 1/16" or less. 1" foam might let you get away with a bit more. But in all honesty, even with 1" foam, anything more than ~1/8" would probably keep me up at night.
The other consideration of not having that deflection braced is that, although it might only be 1/16 now, over time the material may stretch and sag even more.
On the other hand, with a smaller rimmed tank, the rim/bracing may well support the tank just fine regardless of not making full contact with the top all the way around its perimeter.
Hence the need to know much more about the stand and the tank before any can even try to provide a reasonable answer...