Is 'avocardio' a pun?

It's a pun.

The rhetoric site Silva Rhetoricae hosted by BYU and maintained by Dr. Gideon Burton provides the following definition of pun under paranomasia:

Using words that sound alike but that differ in meaning (punning).

In your example, let's break down the words at play:

• avocado, a tree well-known for its edible fruit

• cardio, heart-related activity

• avocardio, the nonce portmanteau from combining avocado and cardio

In this case, the -cado in avocado is echoed in the -cardio in avocardio, which has similar sounds. Avocado and avocardio sound alike. But they have two meanings. Literally the avocado is a fruit, but avocardio plays off of the avocado's perceived status as a heart-healthy food (e.g. "An avocado a day keeps the cardiologist away," Penn State) to create a new word and meaning. That fits the definition of paronomasia.

Now, whether it's a good pun or one where its forced similarity is groan-worthy depends on your aesthetic judgment and your taste in t-shirts.