Dyalog APL, 19 17 16 bytes
≢+#⍎'\d'⎕R'&+',⊢
Takes string and returns
≢ length
+ plus
# in root namespace
⍎ evaluation of
'\d'⎕R'&+' regex append digits with a plus
, followed by
⊢ the unmodified string
–3 thanks to ngn
