My soil is clay-ey as well and I don't know of a bad time to add compost (soil conditioner). I add whenever I have the finish matl. to do so. All my beds & garden get several applications over a year. This is zone 9 with dry hot summers & chilly wet winters (but not this one...) if that makes a difference or not I don't know.
Hope that helps in some way.

Ok so that leads me to another question. Is there a difference between soil conditioners and compost? I would believe that there is, based on the fact that you can buy each separately, but I couldn't back that up with solid evidence. I mean obviously if you're adding compost, you're "conditioning" in a sense, but is there something else to a conditioner?

Compost that I have made is the only conditioner I have ever used so I'm not qualified answer about bagged soil conditioners. I'm sure others will weigh in.

No, there is never a bad time to add "soil conditioners" to soil.
Every "soil conditioner" I have ever looked at is organic matter. Compost s organic matter. The only difference I have ever seen is price with what is labeled "soil conditioner" priced about twice as much as compost.

Is there a bad (or unnecessary/inappropriate) time to add soil conditioner to your garden?

Unless it's compost, yes. Most of the time they are not needed, they are just heavily marketed to people who feel the urge to DO SOMETHING.

I add soil sulfur to my garden because we KNOW we need it to lower pH and unlock some of the iron in the extremely alkaline desert dirt.

But "humic acid", "microbiota", "mycorrhyza mix #9" .... and any and all of those things you attach to the end of a hose and spray on the dirt ... heck no. it's Pixie dust and the only thing it improves is the vendor's bank balance.

If your plants did well, you don't need additives. Start a compost heap, make your own compost and get the urge to do something taken care of that way.

I have a compost pile but it was spread over the garden at the end of the season and tilled under. We also started vermicomposting indoors over the winter but don't have an appreciable amount. I'm thinking with that I might just take a handful of it and put it in the holes as I plant this year.

I totally agree with the 'compost will do the same thing' comments.

And, it's impossible to know whether a product is worthwhile unless you know exactly what is in it, and what condition you are trying to 'treat'.

The bags of "soil conditioner" I buy at Lowes are simply pine bark fines. I have a horse operation so use composted (or mostly but not entirely composted) horse manure and stall leavings on all my beds--perennials, vegetable, roses, foundation planting. Once I have an established bed, I use it in the same way most people use mulch. In areas that need a more finished look I'll top the layer of compost off with the soil conditioner because it is so much more attractive.

Because of my over abundant availability of compost I don't mix soil conditioners into the soil because as others have said the compost can do the same thing and it has added benifits that the conditioner doesn't include. I would think though that a soil conditioner that is wood product might give you some nitrogen tie up issues if too much of it is dug into the soil.

I have also used soil conditioner on perennial gardens as the sole source of mulch. It breaks down quicker than the large wood chunk mulch, but I very much liked the results after several years of using it on top of the soil.