I don't know about other RA-4 replenishers, but the Kodak RA-RT Developer/Replenisher, used to develop at room temperature for two minutes, does not require any starter or dilution after mixing to use as a developer..
I can't vouch for the Kodak product, but at least the Fuji product line (MP60, MP90, etc.) require a starter or need to be seasoned by running a significant amount of (exposed) paper through it. Otherwise color balance cannot be dialed in correctly and contrast is way off; in severe cases there can also be a very pronounced color casts to the whites. Only with starter does the product develop as intended. This is true for trays as well as RT processors.
I would be very surprised if the Kodak product would perform differently in this respect and by sheer magic 'knows' if it's being used for the first time or one shot, or as a replenisher. Regardless of the developer used, there will always be buildup of halides in the developer as it's being used as well as pH drift from an initial state; a starter compensates for this.
Sadly, Kodak does not make information on fresh vs. seasoned tank pH easily available, which is a reasonably good indicator whether the two solutions can be treated as equivalent. For Fuji chemistry, the pH of replenisher is significantly higher than that of a seasoned tank. Kodak does give information on specific gravity, which turns out to be significantly higher for a seasoned tank of developer than the replenisher (z130 page 1-10). While this does not necessarily indicate a similar difference in developer activity, it is highly unlikely that the pure replenisher will perform the same as the developer. Indeed, if this were the case, there would be no need for a starter altogether. Furthermore, the troubleshooting section of Z130 specifically spends attention to the issue of overreplenishment (as well as underreplenishment, obviously). If using the replenisher would somehow yield the same results as a started/seasoned tank, then these precautions would have no basis.
If you're optimistic, you will probably argue that you can filter you way out of the difference between using a replenisher vs. a seasoned/started tank. I'm very, very skeptical of this and my experience with at least the Fuji developer suggests that this is absolutely impossible. While you
can get color development by using just the replenisher without a starter, it is
not possible to get the same color balance as with properly maintained developer chemistry. I'm much more optimistic about using the developer at a sub-standard temperature, which indeed I have done for a long time, and this appears to yield decent results,
provided that filtration is adjusted to account for the difference in developer activity. So also with this factor you don't get exactly the same output.
Its use this way was endorsed by PE
I do recall PE using Ektacolor RA/RT in trays at room temperature, but I do not recall him specifically mentioning only using the replenisher without a starter
or without seasoning it and then replenishing it (which achieves the same as adding the starter). I'm not saying you're wrong; I'm just saying I don't recall this particular aspect of his processing.
I'd also wager to note, at the risk of being accused of sacrilege, that PE's examples of color transparency reversals (he printed slides onto RA4 paper) were admirable, but he described them as "quite good" while in my eyes the examples he showed were mediocre at best. This is not to discredit the vast and insanely useful knowledge base he contributed to the community, but to illustrate that PE himself was also only human, and as a result prone to imperfection just like all of us (although granted, significantly less so when it came to color materials!) and/or that whatever he said was open to some degree of interpretation especially when it came to subjective assessments (i.e. "x or y works well/not so well").
Long story short: if RA4 replenisher works for you in the way you described, that's very nice, but I myself would not recommend it.
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