Were alchemists right?

They were wrong in the same way the people who made human-sized wings to fly were wrong. The goal of flight/metal transmutation is not impossible, but the methodology is naive and hopeless.

There are ways that gold can be produced by radioactivity:

Chrysopoeia, the artificial production of gold, is the symbolic goal of alchemy. Such transmutation is possible in particle accelerators or nuclear reactors, although the production cost is currently many times the market price of gold. Since there is only one stable gold isotope, 197Au, nuclear reactions must create this isotope in order to produce usable gold.

Italics mine.

In a sense the goal of alchemists is reached,but they were aiming at getting gold for its value, not for the fun of it.

Most readers probably are aware of several common claims about alchemy—for example, ... that it is akin to magic, or that its practice then or now is essentially deceptive. These ideas about alchemy emerged during the eighteenth century or after. While each of them might have limited validity within a narrow context, none of them is an accurate depiction of alchemy in general

They were the "chemists " of their time , in their various pursuits.

There are two aspects to this. First, what kind of physical process can transform one chemical element into another. Second, the contribution of alchemy to the development of science.

On the first aspect, the methods employed by the alchemists were, we now know, not going to succeed. But the idea that it might be possible to transform one chemical element into another is not at all a stupid idea. It is a perfectly sound idea. However it turns out that it requires processes that change the atomic nucleus, and this requires either the use of radioactivity or else high-energy collisions. It cannot be done by chemical reactions. So no amount of heating stuff up in ordinary fires or pouring one liquid into another or adding ingredients of this or that is going to work.

On the second aspect, the alchemists made a mixed contribution to the development of science. On the one hand some of their ideas were way off-base. On the other hand some of them, sometimes, took an empirical approach and tried things out, which is good. This provided a counter-balance to other approaches which tried to get at knowledge of the physical world merely by abstract mathematical and philosophical debate. What was needed was a combination which was both empirical and willing to experiment, but also careful about the reasoning and willing to learn and apply mathematical methods. In the medieval period there was a lot of painstaking debate about all kinds of abstruse questions, and sometimes one feels that what they needed to do was just try mixing up a few chemicals and see what happens. So although the alchemists usually were not thinking very clearly, their humble contribution should not be completely dismissed.

To find out more about this you might try the history of science stack exchange.

Thanks to all commenters; I made an adjustment suggested by KRyan.