Is Adwords paid advertising going to push up my organic results?
I am not using paid Google Ads yet just thinking about it. Could my spending on Adwords help get me better rankings also in organic search or is there any correlation between Ads spending and organic rankings?
No, that's not happening. I am not saying this because google says so. There are multiple studies that clearly state that even the biggest adwords spenders do not get any benefits in regular serp.
I've no idea about it and I'm not using.
I think it does but not directly. Consider how your on-page metrics impact organic rankings. If the paid traffic boosts your time on site and pages per session while lowering your bounce rate I am betting you will see organic benefit. Likely it would not be enough to justify the cost of such a campaign.