1. yes you will. that is the answer to the first question.
2. no. you will only get this one when you use RoTP. that is the answer to the second question.
Thanks for the quick reply
50's
Darth Keiv DM/Reg, Crack'ed Justice BS/Reg, Crack'ling Cage Fire/Rad,
Crack'ed Earth SS/Stone, Crack'ed Brawler DM/WP, Crack'ed Legend Axe/WP,
Crack'ed Current SS/Elec,Crack'ed Ice Ice/Kin, Crack'ed Cacophony Son/Son,
Crack'ed Widow SOA, Crack'ed Bully Thugs/Dark, Broil-O Fire/Kin, iCrack'ed DB/WP.
no problem.
A little longer answer:
The LotG +Recharge is a global IO, which means it will work all the time, whether the power is activated or not, and whether the power is available or not. However, if you exempt more than 3 levels below the IO level, you will no longer get the benefit of it.
The Numina regen/recovery, like the other regen/recovery uniques, the Stealth IOs, and a number of other IOs, are often called "proc 120s", because they are, in affect, a proc that has 100% chance to go off and will work for 120 seconds when slotted in a click power that is activated. Slotted in a passive they are always on, in a toggle they are on when the toggle is.
Most people slot the regen/recovery uniques in Health, or another passive power that takes Heal IOs. If on the off-chance you didn't take Health, you will have it when I19 goes live. When exemping, they will work if the power is available to you.
My Characters
Knight Court--A CoH Story Complete 2/3/2012
The Luck of the Gambler is a Global Invention Enhancements. It will act like a set bonus and if you exemp more than 3 levels below the level of the IO, it will cease to give you the recharge bonus (though the defense bonus will still work).
The Numina is a Proc. In a click power, it will start working when the power is clicked and for 120 seconds afterwards. In a toggle, it will work as long as the toggle is on. In an auto power, it will always be on.
edit: I'm too slow 
Global @StarGeek
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FWIW, that's happened to me many, many times.
My Characters
Knight Court--A CoH Story Complete 2/3/2012
2 Questions
1. If I put a luck of the gambler:recharge speed into grant invisibility and never cast it, will I still get the 7.5% recharge speed bonus?
2. If I put a numina's convalescense: +regeneration/+recovery into Rise of the Phoenix and never cast it, will I still get the +regeneration/+recovery from it?
Thanks
50's
Darth Keiv DM/Reg, Crack'ed Justice BS/Reg, Crack'ling Cage Fire/Rad,
Crack'ed Earth SS/Stone, Crack'ed Brawler DM/WP, Crack'ed Legend Axe/WP,
Crack'ed Current SS/Elec,Crack'ed Ice Ice/Kin, Crack'ed Cacophony Son/Son,
Crack'ed Widow SOA, Crack'ed Bully Thugs/Dark, Broil-O Fire/Kin, iCrack'ed DB/WP.