TL:DR - Unlikely :)
Email deliverability to the primary inbox vs the promotional folder or even the spam folder is based on several factors.
First, there are configuration requirements that your ESP should be able to help you with to ensure that ISPs confirm that the sender is actually you. Talk to your ESP about CNAME, DKIM and DMARC and ensure your settings are configured properly.
Secondly, List quality: The ISPs look to email engagement when determining what to do with your email, and where to put it. Make sure your email list is 100% opt in, that you opt out anyone who tells you they want to be removed immediately, and that you scrub unengaged subscribers at a regular cadence.
Lastly, The content of the email will impact deliverability as well. The ISPs look at the subject line for "spammy" content. They scan the copy and of the email to understand look for key words and phrases to determine what type of content the email includes, and they look for the image to text ratio.
Jeeng uses these services to compare the same email creative with and without Jeeng ads, and rarely sees any negative impact from adding our ad units to the template.