The current team would get relegated, however within a few years they would be top 4 and challenging for the title.
Long term success in football in largely driven by money, which is driven by fanbase and marketability. Celtic have one of the biggest fanbases in the UK (60,000 crowd most weeks, at least until recently) and huge global appeal due to the Irish links, and branding. Historically they are probably the biggest club in the UK behind Man Utd and Liverpool, and their decline during the last 15 years has really been due to the collapse of Scottish football. If you put them in the EPL they would be huge.
Rangers would also do well for similar reasons but they don't have the same global appeal that Celtic do, so they would probably be around the level of Spurs.