Let's look at some facts about the support items now.
1. They cost 400 gold for about 1600 gold worth of stats, fully upgraded. Comparatively, Eye of the Aspect (Full upgrade Relic) used to cost 1800 gold for about 1800 gold worth of stats, plus wards, and passive. So you can essentially get +1200g from stats by upgrading your starter item. The stats are a generic health and power boost.
2. They take about 10 minutes of combat to fully upgrade. 5 minutes and you should have your wards on. 10 minutes and your item will be done. Efficient play will speed things along a bit.
3. A fully upgraded item loses its gold assist function. This can be extended briefly by remaining in combat, but the usual maximum gold these items produce is about 1000 gold.
4. Unlike the original support items, you don't receive a combat damage benefit or a health benefit directly from using these items. In other words, Relic Shield cannot be used to passively heal your lanemate, and your harass will be comparatively weaker without Spellthief damage procs.
5. If you kill enough minions (more than 2 per wave) your restriction will kick in, limiting the gold you receive from minions. This is measured over a span of 5 minutes. If you are using an execute item, the minions you kill with your passive will count towards this.
6. Killing all 7 of the minions starting with the casters will be worth 73g with the weakest penalty active. The amount of gold for wiping a minion wave with cannon is at least 165 without a penalty. The penalty will cost your team at least 90 gold per wave you clear, or 3 gold per second. At maximum strength you will receive only 33 gold per wave, a loss of 132 gold for your team.
7. If you kill only a siege minion and a melee minion from each wave, you will make a minimum of 81g. You will make less gold from killing all 7 minions (73g) than from killing just 2 minions.
8. To make up for the 3 gold per second you could be earning by farming minions, you will be awarded 3 gold per 10 seconds by the support item's passive gold generation.
9. Assuming you play perfectly, using Spellthief, farming 2 minions each wave as you go, getting cannons every third wave and then as you can, you will earn 1200g in free stats + 1000g in generated gold + 330g/3 mins from minions to 15 + 18g/min from your item's passive. By 15 minutes, you will have earned around 3700-3800 gold worth of liquid assets and stats. This is roughly equal to maximized farming from a skilled ADC. However, it is more reasonable to assume you will not be killing minions, and your gold will be closer to 2500, which is roughly equal of a mediocre-to-average ADC.
10. When you reach 1000 gold, you can still kill 20 minions without your penalty kicking in. If you just farm waves, you'll get about 370 gold and after 3 waves your passive will switch on, soft-capping your gold to about 2800 at 13 minutes.
11. Assuming you ignore caster minions, you can increase this amount to about 500. Your best bet continues to be killing only 2 minions from each wave.
12. Assuming you planned to make at least 220g per minute from farming waves as a farm support (Zyra, Taric) you will lose at least 100 gold a minute, potentially much more, from keeping your support item. The more you planned to earn, and the worse you adapt, the more you stand to lose. If you do not change your style at all, you will lose 160-220g gold per minute to your support item, with the losses greater the more you planned to earn.
13. Players that do a good job adapting, taking exactly 2 valuable minions per wave, will break even in gold-per-second from their "freebies" around the 40 minute mark, and then start to fall behind. This means always taking cannons away from your allies, and never taking more or less than 2 minions, as well as never killing caster minions.
14. Players that do a bad job adapting and simply kill all the minions will break even as soon as 20 minutes and start to fall behind.
15. Most critically, if your opponent has pushed a double wave into your turret and you clear it (13 minions) and you happen to kill a couple more minions in the meantime, your passive will kick in.