Can using an Octave pedal hurt my amp?

I'm using a Telecaster through a Deluxe 112 amp and was curious whether using an octave pedal to play occasional "1 octave down" riffs when our base player is absent will hurt the speaker in my amp? When I use an octave pedal with my guitar, should I "A-B" switch over to a bass amp?

And on a related topic, if I go the other way and use a bass for those few times I need to play a bass riff, is it safe to put the bass through my guitar multieffects box (an 80s vintage analog Ibanez PUE5) or should I buy a separate bass multieffects box?

Thanks in advance!!

It all depends how robust your speaker is and how much time is spent an octave down, something like a 25 watt celestion won't do as well as 65w with a thicker cone material and larger magnet. If you start getting heavy speaker distortion i would recommend that you switch to another amp or cab, especially if you are going to do it for long periods. (filling in for bassist)
Your effects unit should be fine, bass units are more optimised for the tonal range of the bass but no one really follows the rule.

I've used a Boss OC2 for years, and I've only ever had one instance of damage. I blew a 25 Celestion Greenback about 2 years ago in my Alamo amp.....and that was after using the octave down extensively for a long time (many gigs).

But it sounded so good, that I just put another Greenback in it and I take my chances. Like I said, that was 2 years ago, and still no problems.

I think that the most dangerous area is when you're running 100% clean (no distortion/overdrive pedals) into a low power amp that is cranked to the max.....and then turn your octave pedal on.

I have A/B'ed the signal and run into a bass amp, just like you're talking about, and that's a pretty cool little sound. Run your ABY pedal as the very first thing in your signal chain, then the octave pedal between the ABY and the bass amp. That way you get your thick sustained tone from your amp, and a tight-snappy-poppy tone from the bass amp.

Down side? What guitar player wants to haul around a bass amp? :lol:

Thanks for the replies and actually, I'm pretty lucky because in my situation I'm playing at the same church each week and when the bass player can't make it, his amp is still there (bwahahaha) and all I need to do is bring an A-B switch and extra cable! :)