yes

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2922891/

A BigBed file can contain overlapping intervals

You can use Nezar Abdennur's pybbi library to check this for yourself, for regions of interest:

$ source activate some_environment
(some_environment) $ pip install pybbi
...
(some_environment) $ python
...

Then look for overlaps at a position (or a range):

>>> import bbi
>>> bbi.fetch("measures.optimal.noDupes.LRcheck.bed9.bigBed", "chr3", 25431691, 25431692)
array([8.])

This tells you that there are eight overlapping elements in the specified bigBed file at the single-base position chr3:25431691-25431692. (Because it is single-base, those eight elements must necessarily overlap.)

If you want to know what they are:

>>> list(bbi.fetch_intervals("measures.optimal.noDupes.LRcheck.bed9.bigBed", "chr3", 25431691, 25431692))
[('chr3', 25431673, 25431733, '0.636|TGTGACAACTTCTTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAA', '0', '+', '25431673', '25431733', '254,218,121'), ('chr3', 25431675, 25431735, '0.705|TGACAACTTCTTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAA', '0', '+', '25431675', '25431735', '253,175,74'), ('chr3', 25431682, 25431742, '0.864|TTCTTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAA', '0', '+', '25431682', '25431742', '233,39,31'), ('chr3', 25431683, 25431742, '0.864|TCTTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAA', '0', '+', '25431683', '25431742', '233,39,31'), ('chr3', 25431683, 25431743, '0.864|TCTTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAAA', '0', '+', '25431683', '25431743', '233,39,31'), ('chr3', 25431685, 25431744, '0.886|TTGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAAAA', '0', '+', '25431685', '25431744', '222,22,29'), ('chr3', 25431686, 25431744, '0.905|TGGCCTTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAAAA', '0', '+', '25431686', '25431744', '210,14,32'), ('chr3', 25431691, 25431744, '0.974|TTTTTCCCTGTCTTTTCTCCCTACTCAACACATCAAAAGGAAAAAGAAAAAAA', '0', '+', '25431691', '25431744', '152,0,38')]

All you have to do is iterate over a list of single-base positions over your genome of interest (or some sensible subset) to determine where bbi.fetch returns a positive integer greater than one.

If you fetch over a range wider than a single base than you may need to do operations to check for overlaps within tuples.

BigBed files contain genomic intervals, so it is possible for them to contain overlaps within a file. BigWigs are continuous signal, so you might need to fetch intervals from multiple bigWigs to see if they intersect.