I think yes and no. If Bitcoin quires stable price, then Bitcoin will be used as a reserve currency. On the other hand, if the price is stable, it will cause a decline in interest from speculators, I think so. At least to me it would be in exactly the.
If it stabilizes it will probably reduce the attractiveness of investors entering the Crypto market. So I do not expect that BTC will be stable. Some investors buy BTC just hope that their prices rise to profit. But with price stability, the Crypto market will no longer be attractive.