Unless MTPS has drastically changed in the last 3 years, "TIMS" (read: MPTS) still allows you to move through the program while getting sick. The problem is the last two flights prior to your solo (including your C4390). So if you get sick on FAM 12, you get an ET flight (or an incomplete and refly). If you don't hurl on your FAM 12-2 (excuse me, I mean C4204-2), and don't hurl on your 4390, you're good. "TIMS" has nothing to do with any hold ups.
A stud who shall remain nameless (that's on AW) did that. We went up and he hurled on his FAM 12. However, he completed his flight w/ no other issues. After the FDO and I looked at one another for a little bit figuring out how to code it, we settled on a 4204 COMPLETE, 4204 refly (I forget if that's a 76 ride or not). My stud did fine on the refly and he went on to get jets.