Can a SM receive a Certificate of Achievement/Appreciation from a Battalion from which they are not assigned/attached to?

Yes. Per the awards regulations, anyone who is senior in rank and/or has direct knowledge of actions to be recognized, can submit an award recommendation.

They could when I was on Active Duty SGT (Join to see). I received three Certificates of Achievement and an AAM from Infantry and Artillery Battalions and I was AG Company and not in their unit.

Of course, anyone can thank You for things You did to assist them and show their appreciation with a certificate, letter or both.

Sure can. I got plenty from training other units on communication equipment.

I was a photographer and supported a lot of different units I have certificates and an AAM from other units.

Not sure what Army regs are, but we did it all the time in the Navy.

Absolutely. You can receive coins and AAM's and ARCOM's from other units as well. These things don't have to come from your organization. Hell, you can receive awards from other branches and other countries.

Not only can a sufficiently senior member of another unit, they can also route it through a whatever point in the recipient's command they consider appropriate, silently inviting endorsements.
If I remember correctly, way back when CPL Clardy made Honor Grad for his track at BNCOC, the NCO Academy Commandant routed his letter of commendation through the CG for 101 ABN, which meant that copies of the matching letters from the CG, the 2nd brigade commander and the CO for 1/501 INF also found their way into the young corporal's 201 file.

Yes they can. I wrote up a SGT for an AAM who was in a different battalion than me for going out of his way to help other Soldiers not in his unit. I just sent the 638 to his S1 and they handled the rest, he actually got it too. A Soldier can be recognized by anyone at anytime, it's just kind of expected that your own leadership should be tracking your accomplishments and reward you as appropriate.

I received a COA signed by two LTC's. one MAJ, one CPT, and a MSG and it was not from my unit because of extra duties I took on.

You just have to remember that anyone who is senior in rank or has direct knowledge of the acts committed by the Soldier can recommend an award. It won't always go somewhere, or it might get downgraded, but meeting that criteria anyone can recommend an award.

My son was a Reservist in Iraq and he received an ARCOM from a National Guard unit there. So a certificate for an achievement or appreciation could most certainly be possible. For example, a service member could perform a lifesaving measure (Heimlich maneuver) on a soldier in a totally different unit, or even another base. That would certainly merit such recognition.
In some instances like saving a drowning person, perhaps even a Soldier's Medal if there was risk, or an ARCOM by his/her own unit, or the unit whose service member was saved.
I know of other branches recognizing another branch servicemember awards.
EDITED: I just remembered ... before deploying, he and two others from his Transportation unit, drove tractor trailers loaded with water buffalos to Andrews AFB from Washington, PA for their annual Air Show. While there for a week, the USAF had them act as (unarmed) security beside some of the aircraft. The USAF's most senior NCO there, gave my son his challenge coin - probably his two companions as well.