While this (placebo effect) does hold true it's not something that should be toyed with when using antivenom.
Antivenom can be as harmful to the victim as the bite itself.
Certainly with venomous snake bites (I have some experience here, more than most) the hospital staff wait until they are damn sure you've not had a "dry bite" (bitten but not envenomated) before administering antivenom. suffice to say if you think you've been bitten by a rattlesnake but actualy have not if they slammed 20 vials of antivemon in you you'd be in very nearly as much trouble as someone who HAD been envenomated by a rattler.
Going back to spiders many people have issues because of an alergy to the venom rather than the effects the venom in supposed to have. In these instances anti-venom would be counter productive.
It's also worth noting that some antivenoms are a bit of a myth. again going back to snakes there are many instances of species of snakes not having AV at all and where it does exist there are a scary amount of "catch all" solutions. Certainly just one antivenom covers species as diverse as N.American rattlers, SAmerican pit vipers, indian/asian cobra species and many of Australian venomous snakes. There's just one 'brand' AV for the lot "Polyvalent" and it's a case of works brilliants for X,Y and Z, not so well for A,B or C so cross your fingers folks (if they've not dropped off yet)
Sorry for rambling, but antivenom is never administered "just in case" as this can have consequences as bad as any bite.