Well, if your question is, "will we be able to continue desynthing things in Heavensward," I think it's clear that yes, we can. If you're asking, "will there be new demimateria and an increase in desynth cap and new Careful Desynthesis items and so on in Heavensward," the answer isn't 100% certain, but I would be very surprised if it wasn't true. I'm expecting BC4s and FC4s. I'm expecting a new form of MCD. There will be new fish, and the new fish will have new things obtainable via desynth, even if just one new thing and it's a minion. Almost all new materials have been added to new fish - there are fish for Allagan Silk, Waterproof Cotton, Ferberite, Borax, IV materia, and so on.
There are two ways I feel that BC3s can go. Either there will be new, easier to obtain items that desynth into BC3s, like easy level i65+ crafts or i65+ vendor-bought items, or whatever. Or, there won't be. If there are new, easier to obtain items that desynth into BC3s, the price will drop, possibly tank. If there aren't, the price will go up, even if there aren't new recipes that use them because the glamour items are still desirable (and there are likely to be Primal i95 crafted items for the new classes from what I heard). Even if BC4s exist in 3.0, BC3s are likely to continue to be used. Many items that require BC3s require BC2s as well, and many that use BC2s also use BC1s. If many new items require BC3s, the price will spike upward even if there are new sources for it, but if there are plentiful new sources, the price will then plummet.
It's really hard to predict what's going to happen. Based on trends, I expect the price to spike upward just around 3.0's release even if nothing changes just because people will be buying them up in case they're required for things. After that, it depends on what the limiting factor is for new crafted gear. If it's easier to get the other items needed than the BC3s, and the gear is desirable (for use or vanity), price will keep going up. If the BC3-requiring items have another requirement that's harder to achieve, like if BC4s are required too and only drop from hard-to-obtain items, then the value of BC3s will drop since the demand will be limited by the supply of BC4s or whatever.
Personally, I currently have my BC3s up for higher than the market value. I think I'm going to either take all my BC3s off the market, or raise the price way above the market value. The former is great for watching the market in case of a massive spike in value, the latter is better if there's a massive but brief spike and the value plummets immediately after.
Also, for all we know, in HW, the i90 crafted items like Saurian Leather will be easily obtainable in some manner (maybe we will be able to send retainers out for it even?) making pre-existing crafted items that desynth to BC3s tank in expense, causing a drop in the price of BC3s. There are so many factors, it's hard to tell. I certainly didn't expect the value of FC3s, for instance, to tank hard when 2.4 came out. That was really surprising and probably ruined many people's economic engines (and then fueled others <_<).
So, on that note, what if we get something equivalent, a 6,000 gil Vendor item that desynths to BC3s? That will drop the value by 60-90% in about two days, if that long. If you ditch your stock of BC3s now, you protect yourself from that scenario, but if you hold on to them (or collect more), you could make a fortune if the price/need spikes instead.
Really, in the end, it all comes down to the question: how much do you like gambling? Hate gambling? Dump stock. Like gambling? Build stock. Neutral on the subject? Hold steady, watch the market, and capitalize however you can. (Of course, if you hate gambling, why are you desynthing in the first place...?)