No.
You could not mount enough counterbalance weight on the Three Point Hitch to allow a Backhoe front mounted on a tractor to dig.
Nor are the FEL arms or front axle strong enough to support the weight and strains of Backhoe operation.
Just wondering here: They make skid steer quick attach backhoe attachments for skid steers, do they work on compact tractors?
The answer to your first question is YES. See attached.
The sane answer to your second question is NO. Technically you could but it would tear your FEL to pieces. Do not do it.
Skid Steer Backhoe For Sale | Skid Pro Attachments
Skid steer Backhoe Fronthoe Adjustable Bolt On Thumb Excavator Attachment Bobcat
I would be very leery of the forces placed on the FEL. They do not appear to have swing which is good as far as damage to the FEL goes, but I wonder how functional it would be. You would have to move the tractor to get rid of the dirt to the side.Yes, exactly like that but smaller bucket. If it's small enough and actually sized for a bx and not a 6k lb skid loader would be nice. I also came across tree spade buckets. There was a post a while back with a spade that clamps to existing bucket but that looks like asking to wreck your bucket. A whole new long pointy bucket for digging small trenches would be awesome but an extra function super mini front (backhoe) would be even better.
It would seem that a SMALL backhoe bucket close couple mounted on an FEL SSQA might be viable for shallow trenching jobs. There would be no cylinder, just the bucket facing and attached to the SSQA with maybe a foot or so in between.
The downside to any FEL loader attachment, however, is the lack of visibility. That is another reason I'm attracted to 3PH mounted implements
Edit: I see now that post #5 above is basically what I'm talking about here.
Just wondered the same thing with the new ssqa bucket on kubotas the majority might be to big and heavy but it would he cool to see a mini front mount digger even if it only had a 6" bucket and really short reach. As long as it could be used to dig 12-18" deep trench or load a garden tractor trailer or wheelbarrow it sure would beat digging by hand.

I have a bucket spade (Paulmco from Northern Tool) that fits on my pallet forks. Just used it yesterday to plant another live Chrismas tree. Took me 10 minutes to dig the hole in hard clay. They don't work well, but good enough & cheap enough. More importantly it beats a shovel.
Surprisingly I didn't notice my new L4060 digging the hole any faster than my old L3200 did a couple years ago.
View attachment 543869
I have a bucket spade (Paulmco from Northern Tool) that fits on my pallet forks. Just used it yesterday to plant another live Chrismas tree. Took me 10 minutes to dig the hole in hard clay. They don't work well, but good enough & cheap enough. More importantly it beats a shovel.
Surprisingly I didn't notice my new L4060 digging the hole any faster than my old L3200 did a couple years ago.
View attachment 543869
Interesting thought. And actuallkly I had nothing on my 3pt this weekend on the L4060 (double the weight of my L3200). Generally my weak spot is curling a spoonful of dirt out rather than pushing it into the ground. But pushing it into our hard clay isn't easy. Getting dirt out of the spade in a controlled manner is iffy too. It usually bounces the dirt out back into the hole. But at least it's loose & easy to clean out by hand at that point.This might be a time when you don’t want a back weight.