What effects might an electrolyte leak have on nearby electronic components?
It can be inherently corrosive.
Perhaps more important is that the electrolyte is highly conductive electrically, so if power is applied and electrolyte is spilled on a board it can electrolytically etch away traces if there is voltage between them.
Altered impedances are indeed an effect you may encounter. Here's a story backing up this theory:
I just (sort of) fixed three switch-mode power supplies from the early nineties (HP LaserJet IIIp, power supply made by SONY, date code on the capacitors from early 1991, approximately a good 24 years old as I'm writing this).
None of the three supplies would start at all.
No visual clues of blown components, but a lot of oily liquid was visible around the output capacitors (note that there are both oil- and water-based electrolytes around, with water being far less common because it needs funky additives to prevent corrosion). At first, I didn't pay any further attention to it and checked some of the common things like the start-up resistor on the primary side etc., but when I applied voltage to the output of the +5 V branch of one particular unit using a laboratory supply, it went into current limit and indicated a short across the output.
Guess what:
I checked if the output capacitor itself had an internal short, which I have seen often in the past with similar, old switchers - nope; maybe way out of spec, but not shorted.
There is a crowbar thyristor; I took it out of the board and checked it - nope, everything good, even though crowbar circuits are notoriously unreliable and failure-prone, and everyone knows this.
I checked the z-diode in the crowbar circuit - nope, all good.
After I put all the suspects back into the board: Hooray, no short acorss the output when being tested again with the external supply. And hey... switching action, all outputs good. +5 V OK, +12 V OK, +24 V OK.
Wait... what?! Like, ... for real? Dames en Heren, wat een leuke surprise!
Turns out that while soldering, I must have removed some electrolyte around the z-diode in the crowbar circuit, so it didn't cause false triggering of the thyristor any more.
Oh well. You never stop learning. I have seen electrolytic capacitors fail short, I have seen them fail open (lose all their capacitance), I have seen them cause some small visible corrosion in their neighborhood. But never before have I experienced collateral damage in the form of nearby circuits actually behaving in weird ways.
With two more non-working power supples of the same make and model and age left to check, I just used plenty of ethanol and washed their respecitive circuit boards. They were back to normal right away. Well almost. One stopped working after a while, but a second shower did the trick.
Just to be complete: Yes, the caps need to be replaced. They are certainly out of spec. But for a start, the supplies tested OK after just being washed.
And one last note: The caps had no signs of excessive heat, bulging or venting. Seems like the rubber seal may have degraded over the years and has allowed some electrolyte to escape while the printers just sat around, not having been used a lot recently.
And one very last note: There is a new addition to the list of common troubles with the HP LaserJet IIIp. After more than twenty years of service, we have to add leaking power supply capacitors as #4 to the well-known and established list of #1 - the Error 52 (bad laser scanner driver caused by excessive heat around the BLDC motor controller IC), #2 - the plastic wheel at the clutch for the transfer roller breaking and #3 - the little foam rubber at the electro-magnet for the tray's sheet pick-up going sticky and causing the printer to draw sheets from the tray endlessly. To be fair, #1, #2 and #3 can be considered design flaws because they showed up early, but #4 really is more of a regular wear-out problem and not so much bad component choice; there may be better caps, but the ones used aren't exactly bad, either. 20 years or more is not the worst of all lifetimes you get with electrolytic caps, especially inside of switching power supplies.