Such a convention may be legal in some parts of the world (Europe is more permissive than ACBL). But, I have never heard it played here in Finland (and we are quite permissive with conventions unless playing in an event intended to onboard newbies). I don't have the mileage to say for sure, but my guess is that most players are too partnership oriented to try something like this.
My repertory vs strong clubbers consists of the usual overcalls, the pre-empts, and then selected 2-suited poisons. The point is that a random 1S won't do much against expert opponents. The gains from interference come when you can really jam their auction. To do that you need to find your own fits — you want partner to raise somewhat safely. I guess you could squeeze one such bid into a defensive system, but as (necessarily) it will be a low level call, it won't do much damage alone. I want to increase the chances of partner to continue the interference instead.
Compare the sequences:
- (1C strong)-1S (random)- D (strength, but no 5 card suit)-? What can partner do safely here? Nothing much. Have the opponents been disturbed? Not much, they can start searching for their fits at the two level, and their combined strength makes it safe.
- (1C strong)-2H (hearts and a minor)- D (strength, either exactly 4 spades or more strength)- 4H! What can the opening side do here? The strong clubber needs to take a view on slam hunt right away. 4S is an option, but doesn't really invite partner to continue. When their extra strength is split between the two hands, the opps have a difficult decision.
Even a more modest interference like 1C (=strong)-1D (=natural)-D (=GF strength, 4+3+ in majors or some other meaning), 3D inconveniences the opps. Is 3NT still ok? How to agree on a suit in a forcing manner? True, they now have Double and the cuebid of 4D in their arsenal, but they have been robbed quite a bit of the space to investigate.
So the downside of a random overcall like this is that partner is left equally in the dark. This may be why partnership oriented players dislike it.
There is also the following rule/ethics issue. Unless you bid 1S over an opposing strong 1C every time when you cannot take some other, systemically described action, your partner will gradually learn about your motives and tendencies. When such partnership history builds up, the meaning of the 1S bid will no longer be random, and needs to be disclosed to the opponents (even if undiscussed). This is a grey area, and gives the TD a headache. I'm no bridge lawyer, but I would say, by common sense more than anything else, that an established partnership cannot credibly claim to have "no agreement".