Yes, afaik the transaction will still be on the blockchain only appearing when wallet online and fully synced but as you said i assume you do miss still some transactions. The beauty of RAIN being the rewards are random
Hope this helps
i bought some coins for check how much % stake they give,
but unfortunately my block size is just 2k , and 15 days, no reward
wallet is online 24/7 and fully synced.
should i buy more to increase weight of wallet to get reward?
Probably yes. I have over 30K RAIN staking, getting rewards on average every other day, so I reckon, having 2K will give you the reward on average once a month.